Answer:
a = 156°
b = 132°
c = 108°
Explanation:
The sum of the exterior angles of a polygon equals 360°. The sum of an interior and exterior angle equals 180°. There are two missing exterior angles that you need to find the measure of so we can find the value of x.
First exterior angle is with the 82° interior angle. Subtract from 180 to find the exterior angle.
180 - 82 = 98°
The second exterior angle is with the 134° interior angle. Subtract from 180 to find the exterior angle.
180 - 134 = 46°
Now add all the exterior angles together and set them equal to 360.
x + 2x + 3x +72 + 98 + 46 = 360
6x + 216 = 360
6x + 216 -216 = 360 -216
6x = 144
6x/6 = 144/6
x = 24
No find the exterior angles then subtract each one from 180°.
To find a.
a + x = 180
a + 24 = 180
a + 24 - 24 = 180 - 24
a = 156°
To find b.
b + 2x = 180
b + 2(24) = 180
b + 48 = 180
b + 48 - 48 = 180 - 48
b = 132°
To find c.
c + 3x = 180
c + 3(24) = 180
c + 72 = 180
c + 72 - 72 = 180 -72
c = 108°