(4)(5)(6) geometry
check answers

4) octagon
5) 135
6) 720

Problem 4

x = interior angle
y = exterior angle
x = 3y since "each interior angle...is three times the measure of each exterior angle"

The interior and exterior angles are supplementary, meaning,
x+y = 180
3y+y = 180
4y = 180
y = 180/4
y = 45

So we know that
n = 360/y
n = 360/45
n = 8

You are correct in saying that this is an octagon



Problem 5

x = measure of missing angles

Find the sum of the interior angles
S = 180*(n-2)
S = 180*(5-2)
S = 540
The five interior angles add up to 540 degrees

Add up the five angles, set equal to 540, then solve for x
90+90+90+x+x = 540
2x+270 = 540
2x+270-270 = 540-270
2x = 270
2x/2 = 270/2
x = 135

So you have the correct answer of choice C) 135 degrees



Problem 6

S = 180*(n-2)
S = 180*(6-2)
S = 180*4
S = 720

You have the correct answer. Nice work on all three correct answers.