Question

Given: Line MO bisects angle LMN = 60 degree. Solve for x and find the measure of angle M.

a) x = 30°,M = 60°
b) x = 60°, M = 120°
c) x = 120°, M = 60°
d) x = 30°, M = 30°

Answer 1

To find the measure of angle M and solve for x, we use the fact that line MO bisects the 60-degree angle LMN into two equal parts. Therefore, x equals 30 degrees and the measure of angle M is 60 degrees, making option (a) the correct answer.

Step-by-step explanation:

The student's question is asking to solve for the unknown variable x and to find the measure of angle M given that line MO bisects angle LMN, which has a measure of 60 degrees. Since MO bisects angle LMN, the two angles formed are equal, and because angle LMN is 60 degrees, each of the bisected angles is 30 degrees. Therefore, x is equal to 30 degrees, making the correct answer (a) x = 30°, M = 60°.