Question

1. name the angle pair relationship between 123° and m∠x. explain your reasoning.
2. find m∠x and m∠y in the diagram shown. be sure to show all your work.
3. name the angle pair relationship between 12° and m∠h. explain your reasoning.
4. write an equation to help you find m∠h, then solve for m∠h.

Explanation:

1.

Step1: Identify angle - pair relationship

123° and ∠x are vertical angles. Vertical angles are formed when two lines intersect and are opposite each other. They have equal measures.

Step1: Use vertical - angle property for ∠x

Since 123° and ∠x are vertical angles, m∠x = 123°.

Step2: Use linear - pair property for ∠y

123° and ∠y form a linear pair. A linear pair of angles is supplementary, so m∠y+123° = 180°. Then m∠y=180° - 123° = 57°.

Step1: Identify angle - pair relationship

12° and ∠h are complementary angles. Complementary angles are two angles whose sum is 90°. Here, the two angles together form a right - angle (90°).

Answer:

The angle - pair relationship between 123° and ∠x is vertical angles.

2.