Question

Lines g, h, and I are parallel and m < 2 =129

Answer 1

All angles in this diagram are 51 or 129. See below for a specific angle.

Explanation:

Parallel lines cut by a transversal have specific angle relationships.

• Alternate Interior Angles are angles across the transversal between pairs of parallel lines. These angles are congruent. Example: 3, 6, 7, and 10 are all congruent and are pairs of alternate interior angles. 4, 5, 8, and 9 are congruent as well.
• Alternate Exterior Angles are angles across the transversal outside of the parallel lines. These angles are congruent. Example 2 & 11 are congruent alternate exterior angles. 1 and 12 are another set.
• Supplementary angles are angles which form a line and add to 180. If angle 1 + angle 2 = 180 and angle 2 = 129, then Angle 1+ 129 =180. Angle 1 must be 51 degrees.
• Vertical angles are angles across a vertex. They are congruent. Example: Angle 2 and Angle 3 are both 129.

Using these relationships, the following angles have the following measures:

Angle 1 = 51

Angle 2 = 129

Angle 3 = 129

Angle 4 = 51

Angle 5 =51

Angle 6 = 129

Angle 7 = 129

Angle 8 = 51

Angle 9 = 51

Angle 10 = 129

Angle 11 = 129

Angle 12 = 51