Answers
For this case we have that the area of the kite is given by the area of two triangles, the triangles share the same base of 2 + 2 = 4. One of the triangles has height of 6 and the other has height of 7.
So, the total area is given by:
[tex]A = \frac {1} {2} * 4 * 6 + \frac {1} {2} * 4 * 7\\A = \frac {1} {2} 24+ \frac {1} {2} 28\\A = 12 + 14\\A = 26[/tex]
So, the kite area is 26
ANswer:
Option D
Related Questions
what is the quotient? 4x^2+3x+2 divided by x-3
Answers
For this case, we must build a quotient that, when multiplied by the divisor, eliminates the terms of the dividend until it reaches the remainder.
quotient: [tex]4x + 15[/tex]
Divisor: x-3
Dividend: [tex]4x ^ 2 + 3x + 2[/tex]
Remainder: 47
It must be fulfilled that:
Dividend = Quotient * Divisor + Remainder
Answer:
See attached image
Graph the function.
y = –2x^2 + 6x – 2
Answers
Answer:
Step-by-step explanation:
Determine the principal value of the function: Arc sin(square root of 3/2)
Answers
Answer:
π/3
Step-by-step explanation:
We have to find the principal value of [tex]\text{arc sin}(\frac{\sqrt{3}}{2} )[/tex]
arc sin means sin inverse. The sin inverse is a one to one function with its range between [tex]-\frac{\pi}{2} \textrm{ to } \frac{\pi}{2}[/tex]
The principal value of the arc sin will lie within the above given range.
value of sin (60) or sin([tex]\frac{\pi}{3}[/tex]) is [tex]\frac{\sqrt{3}}{2}[/tex].
[tex]\frac{\pi}{3}[/tex] lies between [tex]-\frac{\pi}{2}\textrm{ and } \frac{\pi}{2}[/tex]
So, from here we can say that the Principal Value of Arc sin(square root of 3/2) is π/3
The principal value of the function Arc sin(√3/2) is,
⇒ π / 3
We have to given that,
⇒ Arc sin (√ 3/ 2)
Since, Value of arc sin lies between - π/2 and π/2.
Hence, The principal value of the function Arc sin(√3/2) is,
⇒ Arc sin(√3/2)
⇒ Arc sin(sin π/3)
⇒ π / 3
Therefore, The principal value of the function Arc sin(√3/2) is,
⇒ π / 3
Learn more about the function visit:
https://brainly.com/question/11624077
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In which direction does the parabola open?
Answers
Answer:
up
Step-by-step explanation:
A graphing calculator, spreadsheet, or web site can help you with this one, or you can simply plot some points on a graph.
___
Only the highest-degree terms matter for answering this question. Leaving the others out, the form is ...
y = x^2
This tells you that y gets more positive for larger and larger values of x, regardless of their sign. Thus the graph of it is U-shaped, opening upward.
The sum of the digits of a two-digit number is 13. The units digit is one more than twice the tens digit. Find the number.
Answers
Answer:49
Step-by-step explanation: 9+4=13 4x2=8 8+1=9
9 is the units digit
4 is the tens digit
A can can be rented for $50 per day with unlimited mileage, or for $40 per day plus 25 cents per mile . For what daily mileages will be unlimited mileage plan save you money ?
Answers
The student council at Sparrowtown High School is making T-shirts to sell for a fundraiser, at a price of $12 apiece. The costs, meanwhile, are $10 per shirt, plus a setup fee of $72. Selling a certain number of shirts will allow the student council to cover their costs. How many shirts must be sold? What will the costs be?
(Algebra 2)
Answers
step by step:
first make an equation with the amount of sold shirts being equal to cost of making them -
12x=10x+72 where x is the number of shirts
then, subtract 10x from 12x to get the variable on the same side -
2x=72
finally, divide by 2 to isolate x
x=36 shirts
to figure out the cost, substitute 36 for x in 10x+72
10(36)+72= 360+72= $432
Using the graph below, select all statements that are true.
A. f(0.6)=0
B. f(-3.2)=-3
C. f(5.1)=5
D. This is the graph of the greatest integer function.
E. This graph is one-to-one.
Answers
Answer:
A. f(0.6)=0
C. f(5.1)=5
D. This is the graph of the greatest integer function.
Step-by-step explanation:
The graph maps each x-value to the largest integer less than or equal to that value. That is the definition of the "greatest integer" function.
The "greatest integer" of -3.2 is -4, so B is not a correct choice. The graph does not pass the horizontal line test, so the function is not one-to-one, and E is not a correct choice.
Answer:
C, D, E
Step-by-step explanation:
Using the table below, write a function rule for the balance in the CD account after any number of years. Let y represent the value of the investment at the end of any year x.
CD/Year
Beginning Balance
Interest Earned
Ending Balance
Savings Account/Year
Beginning Balance
Interest Earned
Ending Balance
1
$700
$22
$722
1
$700
$25.90
$725.90
2
$722
$22
$744
2
$725.90
$26.86
$752.76
3
$744
$22
$766
3
$752.76
$27.85
$780.61
4
$766
$22
$788
4
$780.61
$28.88
$809.49
5
$788
$22
$810
5
$809.49
$29.95
$839.44
Answers
Answer:
y = 700 +22x
Step-by-step explanation:
The CD account balance is 722 after the first year and increases by $22 each year. The function rule is a linear function with a y-intercept of 700 and a slope of $22 per year.
y = 700 +22x . . . . . . ending balance after x years
A national study found that a car's value decreases by 15 percent annually. If the car was purchased for $66,000, how much will the car be worth in 10 years? A. $12,993.71 B. $11,768.35 C. $18,429.50 D. $13,792.14
Answers
Answer:
A. $12,993.71
Step-by-step explanation:
Each year, the car's value is multiplied by 1-0.15 = 0.85. After 10 years, the car's value will be ...
$66,000×0.85^10 ≈ $12,993.71
The ages of sunitha and raseeda are in ratio of 7:8 ten years from now there ages will be 9:10 find there present age
Answers
Answer:
Sunitha: 35Raseeda: 40Step-by-step explanation:
Both numbers of the ratio units used to express the ratio in ten years are 2 higher than at present. Thus, each ratio unit must stand for 5 years. That would make their current ages ...
Sunitha: 7·5 = 35
Raseeda: 8·5 = 40
_____
If you can't figure the answer right away from the change in ratio units, then you may need to write a couple of equations:
s/r = 7/8(s+10)/(r+10) = 9/10These can be translated to standard form, which may make some methods of solution easier:
7r -8s = 09r -10s = 10These have solution (r, s) = (40, 35).
Please Help!! 35 Points!!!
Insert <, >, or = to make the sentence true.
12 __ 25
>
=
Answers
[tex]\frac{1}{2}[/tex] > [tex]\frac{2}{5}[/tex]
The wider/open part of the symbol (aka the mouth) faces the larger number, which in this case is [tex]\frac{1}{2}[/tex].
Hope this helped!
~Just a girl in love with Shawn Mendes
If fis a function and x is an element in its domain, which statement is true about the graph of f?
OA.
The graph of f is the graph of the equation f = x.
OB.
The graph of fis the graph of the equation x = f(y).
OC.
The graph of fis the graph of the equation y = x.
D.
The graph of f is the graph of the equation y = f(x).
Reset
Next
Answers
The right choice here is
"The graph of f is the graph of the equation y = f(x)."
Horizontal and vertical axes of the Cartesian plane are conventionally labeled and referred to as "x" and "y", respectively. When we talk about the graph of f(x) in that context, we usually mean the graph of y = f(x). However, this convention may not be followed in all cases. There may be no "y" label on the graph at all, or the horizontal axis may be labeled something other than "x".
It costs 31.95d + 0.10m dollars to rent a car for d days and drive it m miles. How much does it cost to rent a car for 5 days if the car is driven a total of 600 miles ?
Answers
Answer:
$219.75
Step-by-step explanation:
Just plug in the values
x = final cost
31.95(5) + 0.10(600) = x
159.75 + 60 = x
219.75 = x
I don't understand this. Can someone please help me?
Answers
Answer:
a) 16 in²
b) 20 cm²
Step-by-step explanation:
In any prism, a cross section parallel to parallel faces will have the same shape and area as either of those faces. (That is why we say a prism has a uniform cross section.)
a) The face(s) parallel to the cut plane are squares 4 in on a side, so that is the shape of the cross section. Its area is (4 in)² = 16 in².
__
b) The face(s) parallel to the cut plane are rectangles 4 cm by 5 cm. That is the shape of the cross section. Its area is (4 cm)(5 cm) = 20 cm².
Which products result in a difference of squares? Check all that apply. (5z + 3)(–5z – 3) (w – 2.5)(w + 2.5) (8g + 1)(8g + 1) (–4v – 9)(–4v + 9) (6y + 7)(7y – 6) (p – 5)(p – 5)
Answers
Answer:
(w - 2.5)(w + 2.5)
(-4v - 9)(-4v + 9)
Step-by-step explanation:
* Lets explain what is the a difference of two squares
- If we multiply two binomial and the answer just two terms with
negative sign between them and the two terms are square numbers
we called this answer a difference of two squares
- Examples
# (a + b)(a - b)
- Lets multiply them
∵ (a × a) + (a × -b) + (b × a) + (b × -b)
∴ a² - ab + ba - b²
- Add the like term
∵ ab = ba
∴ -ab + ba = 0
∴ (a + b)(a - b) = a² - b² ⇒ difference of two squares
- From above the difference of two squares appears when we
multiply sum and difference of the same two terms
# (a + b) ⇒ is the sum of a and b
# (a - b) ⇒ is the difference of a and b
* Now lets solve the problem
- In (5z + 3)(-5z - 3)
∵ (5z + 3) ⇒ is the sum of 5z and 3
∵ (-5z - 3) ⇒ is the difference of -5z and 3
∵ 5z ≠ - 5z
∴ They are not the sum and difference of the same two terms
∴ The product result not in a difference of squares
- In (w - 2.5)(w + 2.5)
∵ (w - 2.5) is the difference between w and 2.5
∴ (w + 2.5) is the sum of w and 2.5
∴ They are the sum and difference of the same two terms
∴ The product result in a difference of squares
- In (8g + 1)(8g + 1)
∵ The two brackets are the sum of 8g and 1
∴ They are not the sum and difference of the same two terms
∴ The product result not in a difference of squares
- In (-4v - 9)(-4v + 9)
∵ (-4v - 9) is the difference between -4v and 9
∵ (-4v + 9) is the sum of -4v and 9
∴ They are the sum and difference of the same two terms
∴ The product result in a difference of squares
- In (6y + 7)(7y - 6)
∵ (6y + 7) is the sum of 6y and 7
∵ (7y - 6) is the difference between 7y and 6
∵ 6y ≠ 7y and 7 ≠ 6
∴ They are not the sum and difference of the same two terms
∴ The product result not in a difference of squares
- In (p - 5)(p - 5)
∵ The two brackets are the difference of p and 5
∴ They are not the sum and difference of the same two terms
∴ The product result not in a difference of squares
Answer:
option 2 and 4
Step-by-step explanation:
Which products result in a perfect square trinomial? Check all that apply. (–x + 9)(–x – 9) (xy + x)(xy + x) (2x – 3)(–3 + 2x) (16 – x2)(x2 – 16) (4y2 + 25)(25 + 4y2)
Answers
Answer:
(xy + x)and (xy + x)
(2x - 3) and (-3 + 2x)
(4y² + 25) and (25 + 4y²)
Step-by-step explanation:
* Lets explain the meaning of the perfect square trinomial
- If a binomial multiply by itself, then the answer will be a perfect
square trinomial
- Example: if the binomial (ax + b) multiply by itself, then
(ax ± b)(ax ± b) = (ax)(ax) ± (ax)(b) ± (b)(ax) + (b)(b)
(ax + b)(ax + b) = (ax)² ± 2(axb) + (b)²
∵ (ax + b)(ax + b) = (ax + b)²
∴ (ax ± b)² = (ax)² ± 2(axb) + (b)² ⇒ perfect square trinomial
* From the example above the perfect square trinomial has 3 terms
# 1st term is the square the first term in the binomial
# 2nd term is twice the product of the two terms of the binomial
# 3rd term is the square of the second term of the binomial
* Lets solve the problem
- The product of (-x + 9)and (-x - 9)
∵ -x + 9 ≠ -x - 9
∴ The product of (-x + 9) and (-x - 9) is not a perfect square trinomial
- The product of (xy + x)and (xy + x)
∵ xy + x = xy + x
∴ (xy + x)(xy + x) = (xy + x)²
∵ (ax ± b)² = (ax)² ± 2(axb) + (b)² ⇒ perfect square trinomial
∴ The product of (xy + x) and (xy + x) is a perfect square trinomial
- The product of (2x - 3) and (-3 + 2x)
∵ (-3 + 2x) can be written as (2x - 3)
∴ 2x - 3 = -3 + 2x
∴ (2x - 3)(-3 + 2x) = (2x - 3)²
∵ (ax ± b)² = (ax)² ± 2(axb) + (b)² ⇒ perfect square trinomial
∴ The product of (2x - 3)(-3 + 2x) is a perfect square trinomial
- The product of (16 - x²) and (x² - 16)
∵ 16 - x² can be written as -x² + 16
- If we take -1 common factor from -x² + 16
∴ -x² + 16 = -(x² - 16)
∴ (-x² + 16)(x² - 16) = -(x² - 16)(x² - 16) = -(x² - 16)²
∵ (ax ± b)² = (ax)² ± 2(axb) + (b)² ⇒ perfect square trinomial
∵ -(x² - 16)² = -(x^4 - 32x² + 256) = -x^4 + 32x² - 256
∵ x^4 - 32x² + 256 is perfect square trinomial
∵ -x^4 + 32x² - 256 is not a perfect square trinomial
∴ The product of (16 - x²) and (x² - 16) is not a perfect square trinomial
- The product of (4y² + 25) and (25 + 4y²)
∵ 25 + 4y² can be written as 4y² + 25
∴ 4y² + 25 = 25 + 4y²
∴ (4y² + 25)(25 + 4y²) = (4y² + 25)²
∵ (ax ± b)² = (ax)² ± 2(axb) + (b)² ⇒ perfect square trinomial
∴ The product of (4y² + 25) and (25 + 4y²) is a perfect square trinomial
A chemist wants to mix a 66% alcohol solution with eight liters of 54% alcohol solution to produce a solution that is 65% alcohol. How many liters of the 66% alcohol solution should be used ?
Answers
Answer:
We have 8 liters of 54% alcohol.
We will add "x" liters of 66% alcohol to make "8 +x" liters of 65% alcohol.
54 * 8 + 66 x = 65 (8 + x)
432 + 66x = 520 + 65x
x = 88 liters
Step-by-step explanation:
What is 3/4 times 710?
Answers
Answer:
532.5 or 532[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
3/4 x 710
= 3 x 710 ÷ 4
= 532.5 or 532[tex]\frac{1}{2}[/tex]
Final answer:
To find 3/4 times 710, multiply 710 by 3 to get 2130, then divide that result by 4 to get 532.5. Therefore, 3/4 times 710 equals 532.5.
Explanation:
The question asks for the result of multiplying 3/4 with 710. To perform this calculation we simply take the number 710 and multiply it by the fraction 3/4. Multiplying a whole number by a fraction involves multiplying the numerator of the fraction by the whole number and then dividing the result by the denominator of the fraction.
Here's a step-by-step breakdown:
Multiply the whole number 710 by the numerator of the fraction, 3.710 × 3 = 2130.Divide the result by the denominator of the fraction, 4.
2130 ÷ 4 = 532.5.
Therefore, 3/4 times 710 is 532.5.
He function h(t) = 210 – 15t models the altitude of a hot air balloon over time t, in minutes. Explain what h(10) means in the context of the real-world scenario, and how to find its value.
Answers
Answer:
Step-by-step explanation:
h(10) would be the height of the balloon at 10 seconds
Factor 60x2 – 155x + 100 completely.
A. 5(4x + 5)(3x + 4)
B. (20x – 25)(3x – 4)
C. 5(4x – 5)(3x – 4)
D. (4x – 5)(15x – 20)
Answers
Hey there! Thanks for asking your question here on Brainly.
First, we can factor a 5 out of each term in the trinomial. This leaves us with: 5(12x^2 - 31x + 20)
Second, we need to multiply 12 * 20 and find a factor pair of the product, 240, which equals -31. This factor pair would be -15 and -16. This now leaves us with: 5((12x^2 - 16)(-15x + 20))
Third, we need to simplify each binomial in parenthesis. By doing so, what is left inside of each parenthesis should be the same if this step is done correctly. This leaves us with: 5(4x(3x - 4)-5(3x - 4))
Fourth and finally, we construct our new factored trinomial! The outside number stays, as well as one of the inner parenthesis binomials. Use the terms you factored out of the parenthesis in step three to construct another
binomial. This leaves us with: 5(4x - 5)(3x - 4) and the correct answer is C.
Hope this helps! If there's anything else I can help you with, please let me know! :)
Felicity set the thermostat in her living room to 68°F. The room temperature t, in degrees Fahrenheit, m minutes after the thermostat is activated, satisfies t = 2cos(0.21m) + 68. Determine the period of the function and explain what it represents. Include the maximum and minimum temperatures in your answer.
Answers
Answer with explanation:
Temperature in the living room =68°F
The equation which satisfies ,the room temperature t, in degrees Fahrenheit, m minutes after the thermostat is activated, satisfies
t=2 Cos (0.21 m) +68----------(1)
⇒To determine the period of the function
Z= A cos (sx+q)+r
As period of cos x is 2 π.
So,the given function has period
[tex]=\frac{2\pi}{s}[/tex]
So, the period of function 1, is given by
[tex]=\frac{2\pi}{0.21}[/tex]
⇒The meaning of period of the function is that after every period of [tex]=\frac{2\pi}{0.21}[/tex] the temperature of the room increases or decreases by an integer equal to 2.
⇒Cosine function has maximum value of 1 , and Minimum value of -1.
-1 ≤ Cos x ≤ 1
So, the Maximum value of function = 2 ×1+68°=70°----Maximum Temperature
And, the minimum value of function = 2 ×(- 1)+68°=66°----Minimum Temperature
Final answer:
The period of the cosine function used to model the room temperature controlled by a thermostat is about 29.9155 minutes. This is the time it takes for the temperature to complete one full cycle of oscillation between the maximum of 70°F and the minimum of 66°F.
Explanation:
Felicity set the thermostat in her living room to 68°F. The room temperature t, in degrees Fahrenheit, m minutes after the thermostat is activated, satisfies t = 2cos(0.21m) + 68. This function describes a cosine wave, typical for oscillator systems like a thermostat regulating room temperature. To determine the period of the function, we examine the cosine part of the equation.
The general form of a cosine function is y = A cos(Bx + C) + D, where the period is 2π/B. Here, A is the amplitude, B affects the period, C is the phase shift, and D is the vertical shift. In Felicity's thermostat function, B = 0.21. The period of the function is therefore 2π/0.21, which is approximately 29.9155 minutes. This period represents the time it takes for the room temperature to go from a maximum value back to that value again after one complete cycle.
The max temperature is 2 + 68 = 70°F, and the min temperature is -2 + 68 = 66°F. These represent the highest and lowest temperatures the room will reach with the current thermostat settings.
Please answer this multiple choice question correctly for 30 points and brainliest!!
Answers
Answer:
B. 12n + 2(25) ≤ 100
Step-by-step explanation:
The inequality you are asked for is intended to express ...
shirt cost + pant cost (is less than or equal to) Sandy's budget
The cost of n shirts at $12 each will be 12n. The cost of 2 pants at $25 each is 2(25). Then the inequality is ...
12n + 2(25) ≤ 100 . . . . . matches choice B
Charlie entered an elevator and ride up 10 floors and then down 2 floors before realizing he had not pressed the button for Floor 1. He then pressed the button for Floor 1 and rode down 14 floors and exited the elevator on Floor 1. On which floor did he begin?
Answers
Answer:
Floor 7
Step-by-step explanation:
He entered the elevator on floor x.
Then he rode up 10 floors. Now he is on floor x + 10.
Then he rode down 2 floors. Now he is on floor x + 10 - 2 = x + 8.
Then he pressed the Floor 1 button and rode down 14 floors to Floor 1. Now he is on floor x + 8 - 14 = x - 6 which is the same as Floor 1.
Floor x - 6 is the same as Floor 1, so we get the equation:
x - 6 = 1
Add 6 to both sides:
x = 7
Since we let x be the floor number he entered the elevator in, he entered the elevator on Floor 7.
Answer:
He began on floor 7
Step-by-step explanation:
This is a question where you have to use the question from the end and work your way backwards if that makes sense.
He had to go down 14 floors to get to floor 1. So 14 + 1 = 15. He was on the 15th floor.
Next he went down 2 floors. Since this is reverse, add two floors to the answer. 15 + 2 = 17. He was on the 17th floor.
And finally, he goes up 10 floors. Doing this in reverse, take away 10 floors to the answer. 17 - 10 = 7
He started on the 7th floor.Now to make sure it is correct, start from 7 and follow the original order of the question.
7 + 10 = 17
17 - 2 = 15
15 - 14 = 1
((Please Answer with A B C or D))
If x = 3 inches, what is the perimeter of the figure above?
A. (36[tex]\sqrt{2}[/tex] + 36) inches
B. (6[tex]\sqrt{2}[/tex] + 12) inches
C. 72 inches
D. (6[tex]\sqrt{3}[/tex] + 12) inches
Answers
Answer:
B. (6√2 + 12) inches
Step-by-step explanation:
The length of the kite edge at upper left is ...
x/sin(45°) = x/(1/√2) = x√2
The length of the kite edge at upper right is ...
x/sin(30°) = x/(1/2) = 2x
The perimeter of the kite is double the sum of the lengths of these edges:
P = 2(x√2 +2x) = 2x(√2 +2)
For x=3 in, this is ...
P = 2·(3 in)(√2 +2)
P = (6√2 +12) in
_____
The sine of an angle is the ratio of the side opposite to the hypotenuse. Here, the side opposite is x, and the hypotenuse is the kite edge of interest.
x/hypotenuse = sin(angle)
hypotenuse = x/sin(angle) . . . . . solve for hypotenuse
Answer:
B
Step-by-step explanation:
I was told to put down A B C or D
And B was right
Evaluate the expression.
Answers
Answer:
C
Step-by-step explanation:
at least two have to be in the same place (i think), and that’s the only one that does that
Answer:
55/56 ≈ 0.982143
Step-by-step explanation:
nPk = n!/(n-k)!
Your expression is ...
1 - (6·5·4·3)/(8·7·6·5·4·3) = 1 - 1/(8·7) = 1 - 1/56 = 55/56 ≈ 0.982143
A rectangular garden measures 3 feet by 15 feet the gardener decides to extend the garden 1 foot in each of the four directions what is the perimeter of the new garden in feet
Answers
The perimeter of the new garden after extension is 44 feet.
Explanation:To find the perimeter of the new garden, we need to determine the dimensions after the extension. The original garden measures 3 feet by 15 feet, and the gardener decides to extend it by 1 foot in each direction. This means the new dimensions are 5 feet by 17 feet.
To find the perimeter, we add up all the sides of the rectangle. The formula for the perimeter of a rectangle is:
P = 2(l + w)
where P represents the perimeter, l represents the length of the rectangle, and w represents the width of the rectangle. Plugging in the values, we have:
P = 2(5 + 17) = 2(22) = 44 feet
Therefore, the perimeter of the new garden is 44 feet.
Need help with this one, no clue how to solve this. If someone could explain what's going on like I'm 5 it'd be much appreciated.
Find x.
Answers
Question 10
cos 45 = x/10
cos 45(10) = x
(1/sqrt{2})*10 = x
10/sqrt{2} = x
Rationalize the denominator.
[10/sqrt{2}] • [sqrt{2}/sqrt{2}] = x
10•sqrt{2} ÷ 2 = x
5• sqrt{2} = x
HELP!! I don't understand this question!!
Answers
Answer:
The answer would be c.
Step-by-step explanation:
What I'm understanding from this question is,
In the first attachment, Which has the questions selected on Shows there are two shapes.
Those two shapes have to go in to the identify the tessellation Created using the given regular polygons.
As you can see in answer C. Both shapes are represented in that tessellation.
For example, In the attachment below ] I will be showing you an example of what the question might look like for This certain tessellation.
You obviously know that square is tiltedMake a diamond shaped. That is why the diamond and hexagon is correct!
hope this helps! if it helps in any way plz mark as branliest !
If this helped in any way, can I have brainliest? Please and thank you.
Need help with this math question
Answers
Answer:
120
Step-by-step explanation:
If those 2 polygons are similar, then their corresponding angles are the same. The thing that makes them similar as opposed to congruent is that their side lengths exist in proportion to one another instead of being the same.
Answer:
[tex]w = 120\°[/tex]
Step-by-step explanation:
In this case we know that
ABCD and FECG are similar polygons.
This means that their sides are proportional and their corresponding angles are equal.
So if the lines FG and AD are parallel and of proportional length then by definition the angle w is equal to 120 °
Thus
[tex]w = 120\°[/tex]