Multiple choice

In △LMN, the bisectors of ∠L and ∠N intersect at an angle of 112∘. What is the measure (in degrees) of ∠M ?

  1. 62

  2. 60

  3. 44

  4. 72
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C Correct answer
Explanation

In any triangle, the angle formed by the intersection of two angle bisectors is related to the third angle. The formula is: intersection angle = 90° + (third angle)/2. Given the intersection is 112°, we have 112° = 90° + M/2, which gives M/2 = 22°, so M = 44°. This relationship holds because angle bisectors create specific angle relationships in triangles.

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