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:

Step1: Identify angle - pair relationship for 123° and ∠x

123° and ∠x are vertical angles. Vertical angles are formed by two intersecting lines and are opposite each other. They are congruent.

Step2: Find m∠x and m∠y

Since 123° and ∠x are vertical angles, m∠x = 123°.
123° and ∠y are supplementary angles (they form a linear - pair, and the sum of angles in a linear - pair is 180°). So, m∠y=180° - 123° = 57°.

Step3: Identify angle - pair relationship for 12° and ∠h

12° and ∠h are complementary angles. Complementary angles are two angles whose sum is 90°.

Step4: Write and solve the equation for m∠h

The equation is 12°+m∠h = 90°.
To solve for m∠h, we subtract 12° from both sides of the equation: m∠h=90° - 12° = 78°.

Answer:

1. The angle - pair relationship between 123° and ∠x is vertical angles. Reason: They are opposite each other formed by two intersecting lines and are congruent.
2. m∠x = 123°, m∠y = 57°
3. The angle - pair relationship between 12° and ∠h is complementary angles. Reason: The sum of the two angles is 90°.
4. Equation: 12°+m∠h = 90°, m∠h = 78°