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

44

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 \({44}^\circ\).