Question

In $∆$ABC, bisectors of $\angle$A and $\angle$B intersect at point O. If $\angle$C = 70^° . Find measure of $\angle$AOB.

Answer 1

If the bisectors of ∠X and ∠Y of a △XYZ intersect at point O, then $\angle \mathrm{XOY}=90°+\frac{1}{2}\angle \mathrm{XZY}$
$$\begin{gathered} \therefore \angle \mathrm{AOB}=90°+\frac{1}{2}\angle \mathrm{ACB} \\ =90°+\frac{1}{2}\left(70°\right) \end{gathered}$$
= 90^∘ + 35^∘
= 125^∘
Hence, the measure of ∠AOB is 125^∘.