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.
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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