Answer:
5(4+√3)/13
Step-by-step explanation:
Answer:
15) For a regular polygon of N sides, the measure of one interior angle is:
A = (N - 2)*180°/N
In this case, the figure has 11 sides, then we have N = 11, and the measure of each interior angle will be:
A = (11 - 2)*180°/11
A = 9*180°/11 = 147.27°
Rounding to the first decimal after the decimal point, we get:
A = 147.3°
Then the correct option is B.
16) We know that the length of all the sides of a square is the same.
In the image, we can see that the length of the right side is 4, and the length of the top side is 2x + 4
And those lengths must be the same, then we have the equation:
2x + 4 = 4
subtracting 4 in each side of the equation we get:
2x + 4 - 4 = 4 - 4
2x = 0
The only solution for this equation is x = 0.
Then the correct option is C
Check out the attached image below. I added a variable y to help find x
tan(angle) = opposite/adjacent
Focusing on the smaller 30-60-90 triangle, we see that
tan(60) = 91/y
y*tan(60) = 91
y = 91/tan(60)
y = 52.53887
now focus on the largest triangle and we see that
tan(30) = 91/(x+y)
0.57735 = 91/(x+52.53887)
0.57735*(x+52.53887) = 91
0.57735*x + 0.57735*52.53887 = 91
0.57735*x + 30.3333165945 = 91
0.57735*x + 30.3333165945 - 30.3333165945 = 91 - 30.3333165945
0.57735*x = 60.6666834055
x = 60.6666834055/0.57735
x = 105.07782697757
x = 105.1
So the final answer is approximately 105.1