Question

In the figure, $\angle A={60}^o$ and $\angle ABC={80}^o$, find $\angle$DPC and $\angle$BQC respectively.

Answer 1

Given, $\angle A={60}^{\circ }$

$\angle ABC={80}^{\circ }$

To find $\angle DPC$ & $\angle BCQ$

Now, $\angle ADC={100}^{\circ }$[opposite angles of cyclic quadrilateral are supplementary]

$\therefore \angle PDC={80}^{\circ }$

Similarly, $\angle PCD={60}^{\circ }$

$\therefore \angle DPC={180}^{\circ }-{80}^{\circ }-{60}^{\circ }={40}^{\circ }$

Now, $\angle CBQ={100}^{\circ }$

$\angle BCQ={60}^{\circ }\Rightarrow \angle Q={20}^{\circ }$