Question

In Fig. 8, ∠AOC ≅ ∠PYR and ∠BOC ≅ ∠QYR. Name the angle which is congruent to ∠AOB.

Answer 1

$$\begin{gathered} \angle AOC\cong \angle PYR..........\left(i\right) \\ Also,\angle BOC\cong \angle QYR \\ Now,\angle AOC=\angle AOB+\angle BOCand\angle PYR=\angle PYQ+\angle QYR \\ Byputtingthevalueof\angle AOCand\angle PYRinequation\left(i\right),weget: \\ \angle AOB+\angle BOC\cong \angle PYQ+\angle QYR \\ \angle AOB\cong \angle PYQ(\angle BOC\cong \angle QYR) \\ Hence\angle AOB\cong \angle PYQ \end{gathered}$$