Question

Base your answer to the following question on the diagram shown and the given information.

Answer 1

A

Explanation:

1. Line l is cut by line a (let it be named a, because the figure doesn't show its name). Angles 1 and 6 are vertical, so they are congruent.

2. Line m is cut by line a. Angles 3 and 8 are vertical, so they are congruent.

3. Parallel lines l and m are cut by transversal a. Angles 6 and 3 are congruent as alternate interior angles.

Hence,

`3x+25=4x-17,\\ \\3x-4x=-17-25,\\ \\-x=-42,\\ \\x=42^(\circ).`

4. The measure of angle 6 is

`3x+25=3\cdot 42+25=126+25=151^(\circ).`

5. Angles 6 and 2 are supplementary angles, so they add up to 180°:

∠2=180°-∠6=180°-151°=29°