Question

In Fig., $\angle P={52}^{\circ }and\angle PQR={64}^{\circ }$, if $QO$ and $RO$ are the angle bisectors of $\angle PQR$ and $\angle PRQ$ respectively, then find the values of $\angle x$ and $\angle y$.

Answer 1

QO and RO are angle bisecter of $\angle PQR\&\angle PRQ$ respectively so $\angle PQO=\angle OQR$ .

$\angle OQR=\frac{1}{2}\angle PQR=32$

Now in $\Delta PQR$ ,$\angle PRQ=180-(52+64)$

$=180-\left(116\right)$

$=64$

$y=\frac{1}{2}\angle PRQ=32$

Now in $\Delta OQR=32+x+32=180$

$x=180-64$

$x=116$