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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

Respuesta :

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:

  1. 5x-21 = (5*27) - 21 = 135 - 21 = 114
  1. 2x+12 = 2 * 27 + 12 = 54+12 = 66

And sum = 114+66= 180  

To learn more about exterior angles from the given link:

https://brainly.com/question/26969915

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