Question

A fence on a hill uses vertical posts L and M to hold parallel rails N and P. If m∠1 = 6x and m∠12 = 4x, then what is the measure of ∠5?

Answer 1

Answer;

D: 108 degrees

Answer 2

Measure of ∠5 is 108°

Explanation:

Given m∠1 = 6x and m∠12 = 4x, we have to find the measure of ∠5.

As ∠1 and ∠5 are alternate exterior angle hence equal i.e ∠1=∠5

Also, ∠5 and ∠12 are co-interior angles ∴these are supplementary

⇒ m∠5+m∠12=180°

⇒ 6x+4x=180°

⇒ 10x = 180° ⇒ x=18

∴ m∠5 = 6x = 6(18) = 108°

Hence, measure of ∠5 is 108°