Question

1. find all of the angle measures that are created by a transversal crossing parallel lines. tell which theorem you used.
2. 2) 3) 4) 5) 6) 7)
3. 9) 10) 11) 12) 13) 14)

Explanation:

Step1: Identify angle - relationships

When two parallel lines are cut by a transversal, vertical - angles are equal, corresponding angles are equal, alternate - interior angles are equal, and alternate - exterior angles are equal, and same - side interior angles are supplementary (sum to 180°).

Step2: For the left - hand figure

Given an angle of 110°.

• The vertical angle to the 110° angle is also 110°.
• The corresponding angles to the 110° angle are 110°.
• The alternate - interior angles to the 110° angle are 110°.
• The alternate - exterior angles to the 110° angle are 110°.
• The same - side interior angles to the 110° angle are 180 - 110=70°.

Step3: For the right - hand figure

Given a 90° angle.

• The vertical angle to the 90° angle is 90°.
• The corresponding angles to the 90° angle are 90°.
• The alternate - interior angles to the 90° angle are 90°.
• The alternate - exterior angles to the 90° angle are 90°.
• The same - side interior angles to the 90° angle are 180 - 90 = 90°.

Answer:

In the left - hand figure: Angles equal to 110° are vertical, corresponding, alternate - interior, and alternate - exterior angles; angles equal to 70° are same - side interior angles. In the right - hand figure: All related angles (vertical, corresponding, alternate - interior, alternate - exterior, and same - side interior) are 90°.