Answer:
15) x = 155°
16) x = 115°
Explanation:
The theorem that relates an exterior angle of a triangle to the opposite (remote) interior angles is helpful for these problems. It says the exterior angle is equal to the sum of the remote interior angles.
15)
Remove the altitude line and consider the interior angle of the triangle next to the exterior angle marked 60°. That interior angle will be ...
180° -60° = 120°
Then the angle we just found and the one marked 35° are "remote" to the exterior angle marked x. The theorem cited at the beginning tells us ...
x = 35° +120°
x = 155°
16)
Extend the left side of the "parallelogram" (the side with the arrow) upward until it meets the top horizontal line. This cuts off a triangle with an exterior angle marked x, an interior angle marked 50°, and another remote interior angle at the top edge of that triangle.
The opposite angles of a parallelogram are congruent, so the external angle to the triangle at the top edge will be x, and the adjacent interior angle in the triangle will be (180° -x).
The exterior angle (x) is equal to the sum of the remote interior angles (50° and (180° -x)), so we have ...
x = 50 +(180 -x)
2x = 230 . . . . . . add x, simplify
x = 115 . . . . . . . divide by 2
The measure of the angles marked x is 115°.