Question 7: In ∆ABC, bisectors of ∠A and ∠B intersect at point O. If ∠C = 70° . Find measure of ∠AOB.

Question 7: In ∆ABC, bisectors of ∠A and ∠B intersect at point O. If ∠C = 70^° . Find measure of ∠AOB.

Answer: 

If the bisectors of ∠X and ∠Y of a △XYZ intersect at point O, then ∠XOY=90°+12∠XZY$\mathrm{}\frac{\mathrm{}}{\mathrm{}}$
∴∠AOB=90°+12∠ACB=90°+12(70°)$$\begin{gathered} \mathrm{}\frac{\mathrm{}}{\mathrm{}} \\ \mathrm{}\frac{\mathrm{}}{\mathrm{}}\left(\mathrm{}\right) \end{gathered}$$
= 90∘ + 35∘ 
= 125∘  
Hence, the measure of ∠AOB is 125∘.