Question

(7)(8)(9) Geometry Check Ans 7) s = 15 8) y = 64 x = 99 9) 96

Answer 1

Problem 7: Correct
Problem 8: Correct
Problem 9: Correct

The steps are below if you are curious

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Problem 7

S = 180*(n-2)
2340 = 180*(n-2)
2340/180 = n-2
13 = n-2
n-2 = 13
n = 13+2
n = 15

I'm using n in place of lowercase s, but the idea is the same. If anything, it is better to use n for the number of sides since S already stands for the sum of the interior angles. I'm not sure why your teacher decided to swap things like that.

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Problem 8

First find y
y+116 = 180
y+116-116 = 180-116
y = 64

which is then used to find x. The quadrilateral angles add up to 180*(n-2) = 180*(4-2) = 360 degrees
Add up the 4 angles, set the sum equal to 360, solve for x

x+y+125+72 = 360
x+64+125+72 = 360 ... substitution (plug in y = 64)
x+261 = 360
x+261-261 = 360-261
x = 99

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Problem 9

With any polygon, the sum of the exterior angles is always 360 degrees

The first two exterior angles add to 264. The missing exterior angle is x
x+264 = 360
x+264-264 = 360-264
x = 96