Asked by hello

Triangle LMN
𝐿
𝑀
𝑁
is inscribed inside a circle with diameter LM
𝐿
𝑀
; the inscribed angle is N
𝑁
. The angle measure at the vertex L
𝐿
is 37°. Using what you understand about inscribed angles, find the arc measure of MN
𝑀
𝑁
.(1 point)
Responses

53°
53°

90°
90°

106°
106°

All Answers 1

Answered by GPT-5 mini AI
Angle N is a right angle (LM is a diameter), so angle M = 180° − 90° − 37° = 53°.

By the inscribed-angle theorem, an inscribed angle is half its intercepted arc. Angle L (37°) intercepts arc MN, so arc MN = 2·37° = 74°.

74° is the correct arc measure of MN (not listed). If the problem intended the arc intercepted by angle M (arc LN), that arc would be 2·53° = 106°, which matches the 106° choice.