Question

problem 10

1. what angle pair is shown in the diagram? find the measure of ∠x.
2. what theorem can you use to find the measure of ∠y using ∠x? find the measure of ∠y.

Explanation:

Step1: Identify angle - pair type

The 105° angle and ∠x are a linear - pair of angles. A linear pair of angles are adjacent angles that form a straight line, and their sum is 180°.

Step2: Calculate the measure of ∠x

Let the measure of ∠x be \(x\). We know that \(105^{\circ}+x = 180^{\circ}\). Solving for \(x\), we get \(x=180^{\circ}- 105^{\circ}\).
\(x = 75^{\circ}\)

Step3: Identify the theorem for finding ∠y

The 105° angle and ∠y are corresponding angles. Corresponding angles formed by a transversal intersecting two parallel lines are congruent.

Step4: Calculate the measure of ∠y

Since the 105° angle and ∠y are corresponding angles and the lines are parallel, \(y = 105^{\circ}\)

Answer:

1. The angle - pair is a linear pair. The measure of ∠x is \(75^{\circ}\).
2. The theorem is the Corresponding Angles Theorem. The measure of ∠y is \(105^{\circ}\).