Answer:
All angles are 113 or 67. See below for each angle measure.
Step-by-step explanation:
Parallel lines cut by a transversal have several angle relationships which can be used to find an unknown angle measure:
• Alternate Interior Angles are angles across the transversal between pairs of parallel lines. These angles are congruent. Example: 8 and 4 are congruent and are pairs of alternate interior angles. 7 and 3 are another set.
• Alternate Exterior Angles are angles across the transversal outside of the parallel lines. These angles are congruent. Example 1 & 5 are congruent alternate exterior angles. 2 and 6 are another set.
• Supplementary angles are angles which form a line and add to 180. If angle 1 + angle 2 = 180 and angle 1 = 113, then 113 + Angle 2 =180. Angle 2 must be 67 degrees.
• Vertical angles are angles across a vertex. They are congruent. Example: Angle 2 and Angle 8 are both 67.
Using these relationships, the following angles have the following measures:
Angle 1 = 113
Angle 2 = 67
Angle 3 = 113
Angle 4 = 567
Angle 5 =113
Angle 6 = 67
Angle 7 = 113
Angle 8 = 67
