Question

The figure to the right shows two parallel lines intersected by a transversal.

Let x = 103°. Find the measure of each of the other seven angles.

Answer 1

77°

Explanation:

103° + ∠1° = 180°

Answer 2

The measure of each of the other seven angles can be found by using the properties of angles formed by parallel lines and a transversal.

The figure to the right shows two parallel lines intersected by a transversal. Since the two parallel lines are intersected by a transversal, the alternate interior angles, alternate exterior angles, corresponding angles, and consecutive interior angles are congruent. Using this information, we can find the measure of each of the other seven angles.

Given that x = 103°, we can find the measures of the other angles as follows:

1. The angle below x and between the two parallel lines is also 103° (alternate interior angle).
2. The angle above x and between the two parallel lines is also 103° (alternate exterior angle).
3. The angle on the top left corner is 77° (corresponding angle).
4. The angle on the top right corner is 77° (corresponding angle).
5. The angle on the bottom left corner is 103° (consecutive interior angle).
6. The angle on the bottom right corner is 103° (consecutive interior angle).