2. In the figure, x is an exterior angle to the triangle below. (a) Explain why x is equal to the sum of the measures of the two nonadjacent interior angles. You need to present the algebra that proves this theorem.
(b) What is m

a) Exterior Angle Theorem

b) x = 109°

Step-by-step explanation:

For a, you can thank the Exterior Angle Theorem. Since the angles of a triangle equal 180°, we can figure out what the third interior angle's measurement is, then subtract that from 180 to get the exterior angle's measure. Since the two angles labeled (64° and 45°) will make an obtuse angle, then the third interior is an acute angle. Add 64 and 45 to get the exterior angle's measurement of 109 degrees. That would mean the third interior angle's measurement would be 71 degrees. 64 + 45 + 71 = 180, so this is true.

(I had used the HSEAT to explain this.)