Question

In the figure, line L1 is parallel to line L2. If the measure of ∠4 = 144°, what is the measure of ∠6 and why? A. 144°, vertical angles have the same measure B. 144°, corresponding angles have the same measure C. 36°, same side interior angles are supplementary D. 36°, alternate exterior angles are supplementary

Answer 1

The measure of ∠6 is 36°

Option C is correct

Explanation:

`\text{Given the figure line } L_1 \text{ is parallel to line }L_2.`

`\text{If the measure of }\angle 4 = 144\°`

we have to find the measure of ∠6

Since ∠4 and ∠6 angles formed on the same side interior angles and the same-side interior angles that are formed are supplementary, or add up to 180 degrees.

∴ ∠4+∠6=180°

144°+∠6=180°

∠6=180-144=36°

Hence, the measure of ∠6 is 36°

Therefore option C is correct.