Question

In the figure, if $BP\left|\right|CQ$ and AC= BC, then the measure of x is

Answer 1

In the figure, AC=BC,$BP\left|\right|CQ$

$\because BP\left|\right|CQ$

$\therefore \angle PBC=\angle QCD$

$\Rightarrow {20}^{\circ }+\angle ABC={70}^{\circ }$

$\Rightarrow \angle ABC={70}^{\circ }-{20}^{\circ }={50}^{\circ }$

$\because BC=AC$

$\therefore \angle ACB=\angle ABC$

(Angles opposite to equal sided)

=${50}^{\circ }$

Now in $\Delta ABC,$

Ext. $\angle ACD=\angle B+\angle A$

$\Rightarrow x+{70}^{\circ }={50}^{\circ }+{50}^{\circ }\Rightarrow x+{70}^{\circ }={100}^{\circ }$

$\therefore x={100}^{\circ }-{70}^{\circ }={30}^{\circ }$