Question

In the figure 1.79 if $\angle$AOC $\cong$ 45$°$ $\angle$BOD = 60$°$ and $\angle$AOB $\cong$$\angle$COD then find $\angle$BOC.

Answer 1

Given:
$$\begin{gathered} \angle \mathrm{AOC}\cong \angle \mathrm{BOD} \\ \angle \mathrm{AOB}\cong \angle \mathrm{COD} \\ \angle \mathrm{AOB}=45° \\ \angle \mathrm{BOD}=60° \end{gathered}$$

$$\begin{gathered} \mathrm{Also},\angle \mathrm{AOB}=\angle \hspace{0.17em}\mathrm{COD}=45°\left(\mathrm{Given}\right) \\ \mathrm{Then},\angle \mathrm{BOD}=\angle \mathrm{BOC}+\angle \mathrm{COD} \\ \Rightarrow 60°=\angle \mathrm{BOC}+45° \\ \therefore \angle \mathrm{BOC}=15° \end{gathered}$$