Question

problem 7

1. what angle pair is shown in the diagram? find the measure of ∠x.
2. ∠x and ∠y are alternate interior angles. how did you move your hand to find ∠y?
3. find the measure of ∠y.
4. what is the name of the angle pair formed by ∠z? find the measure of ∠z. show your steps.

Explanation:

Step1: Identify angle - pair for ∠x

The 55 - degree angle and ∠x are corresponding angles. Since corresponding angles are equal when two parallel lines are cut by a transversal, ∠x = 55°.
$∠x=55^{\circ}$

Step2: Understand motion for ∠y

To find ∠y from ∠x (alternate - interior angles), you can slide your hand along the transversal between the two parallel lines.

Step3: Find measure of ∠y

Since ∠x and ∠y are alternate - interior angles and alternate - interior angles are equal when two parallel lines are cut by a transversal, ∠y = 55°.
$∠y = 55^{\circ}$

Step4: Identify angle - pair for ∠z

∠y and ∠z are a linear pair. A linear pair of angles is supplementary, meaning they add up to 180°.
Let ∠y = 55°. Then, to find ∠z, we use the formula ∠y+∠z = 180°.
$∠z=180^{\circ}-\angle y$
Substitute ∠y = 55° into the formula:
$∠z=180 - 55=125^{\circ}$

Answer:

1. The angle - pair for ∠x is corresponding angles, and ∠x = 55°.
2. Slide your hand along the transversal between the two parallel lines.
3. ∠y = 55°.
4. The angle - pair for ∠z is a linear pair with ∠y, and ∠z = 125°.