Question

Solve for m
10°


30°


45°


60°

Answer 1

Answer: 30 degrees

Work Shown

The two arc measures add to 180 degrees

(arc LM) + (arc MN) = 180

(13x-10) + (7x-10) = 180

20x-20 = 180

20x = 180+20

20x = 200

x = 200/20

x = 10

Then,

arc MN = 7x-10

arc MN = 7*10-10

arc MN = 60 degrees

Use the inscribed angle theorem to divide that amount in half to get,

angle NLM = (1/2)*(arc MN)

angle NLM = (1/2)*(60)

angle NLM = 30 degrees