In ΔLMN, the bisectors of ∠L and ∠N intersect at an angle of 112°. What is the measure (in degrees) of ∠M?
Answer & explanation
Correct answer: option 3
In, \(\Delta \)LMN, ON is the bisector of ∠N and OL is the bisector of ∠L
∠NOL= 112°
So, ∠NOL = \({90}^\circ\) + ∠\(\frac{M}{2}\)
⇒ \({112}^\circ\) = \({90}^\circ\) + ∠\(\frac{M}{2}\)
⇒ ∠\(\frac{M}{2}\) = \({112}^\circ\) - \({90}^\circ\)
⇒ ∠\(\frac{M}{2}\) = \({22}^\circ\)
⇒ ∠M = \({22\; × \;2}^\circ\)
⇒ ∠M = \({44}^\circ\)
Therefore, ∠M is \({44}^\circ\).