Question

In the Fig. lines PQ and RS intersect each other at point O. If $\angle POR:\angle ROQ=5:7$, Find all the angles.

Answer 1

$\angle POR+\angle ROQ={180}^o$ (Linear pair of angles)

But $\angle POR:\angle ROQ=5:7$ (Given)

Therefore, $\angle POR=\frac{5}{12}\times 180={75}^o$

Similarly, $\angle ROQ=\frac{7}{12}\times 180={105}^o$

Now, $\angle POS=\angle ROQ={105}^o$ (Vertically opposite angles)

and $\angle SOQ=\angle POR={75}^o$ (Vertically opposite angles)