Question
In Figure, $\angle\text{POQ}\cong\angle\text{ROS}$, can we say that $\angle\text{POR}\cong\angle\text{QOS}$ 
✓
Answer
We have, $\angle\text{POQ}\cong\angle\text{ROS}\ ...(\text{i})$
Also, $\angle\text{ROQ}\cong\angle\text{ROQ}$ (same angle)
Therefore, adding $\angle\text{ROQ}$ to both sides of $(i)$,
we get: $\angle\text{POQ}+\angle\text{ROQ}\cong\angle\text{ROQ}+\angle\text{ROS}$
$\therefore\angle\text{ROQ}\cong\angle\text{ROQ}$ Hence proved.
Also, $\angle\text{ROQ}\cong\angle\text{ROQ}$ (same angle)
Therefore, adding $\angle\text{ROQ}$ to both sides of $(i)$,
we get: $\angle\text{POQ}+\angle\text{ROQ}\cong\angle\text{ROQ}+\angle\text{ROS}$
$\therefore\angle\text{ROQ}\cong\angle\text{ROQ}$ Hence proved.
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