Triangle LMN 𝐿 𝑀 𝑁 is inscribed inside a circle with diameter LM 𝐿 𝑀 ; the inscribed angle is N 𝑁 . The angle

Question

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°

GPT-5 mini · Answer

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.

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