Answer:
D) 119°
C) The two angles are supplementary.
Explanation:
First problem:
<1 is an exterior angle of the triangle.
<A and <B are interior angles of the triangle far from <1.
For <1, angles A and B are called remote interior angles.
Theorem:
The measure of an exterior angle of a triangle is equal to the sum of the measures of its remote interior angles.
m<1 = m<A + m<B
m<1 = 87° + 32°
m<1 = 119°
Answer: D) 119°
Second problem:
AB is a line. The diagonal line intersects line AB forming 4 angles, a, b, c, and d. Angles c and d are next to each other, called adjacent angles, and have a common side, and the other two sides lie on line AB. That makes angles c and d a "linear pair." Two angles in a linear pair have measures that add to 180°, so angles c and d are supplementary angles.
Answer: C) The two angles are supplementary.