Two alternate exterior angles are formed by a transversal through two parallel lines. If one of these alternate exterior angles has an angle measure of , and the other angle has a measure of , then what is the sum of their angle measures

Answers

The sum of the angle measures of the exterior angles is 180.

What is an exterior angle?

The exterior angle refers to the angle between a side of a polygon and an extended adjacent side.

Now, given that 5x-21 and 2x+12 are two alternate exterior angles. We know that the sum of the two exterior angles is 180° because the two exterior angles are lying on a straight line and straight line is 180°.

Thus, (5x-21)+(2x+12) = 180°

=> 5x-21+2x+12 = 180

=> 5x+ 2x -21 +12 = 180

=> 7x – 9 = 180

=>7x = 189

=> x = 189/7 = 27

Hence the angles are:

5x-21 = (5*27) – 21 = 135 – 21 = 114

2x+12 = 2 * 27 + 12 = 54+12 = 66

And sum = 114+66= 180

To learn more about exterior angles from the given link:

exterior anglesis 180.## What is an exterior angle?

exterior anglerefers to the angle between a side of a polygon and an extended adjacent side.alternate exterior angles. We know that the sum of the twoexterior anglesis 180° because the twoexterior anglesare lying on a straight line and straight line is 180°.exterior anglesfrom the given link: