Question

Question 1
In the given figure, sides QP and RQ of $\Delta PQR$ are produced to point S and T respectively, If $\angle SPR={135}^{\circ }and\angle PQT={110}^{\circ }$, find $\angle PRQ.$

Answer 1

It is given that,
$\angle SPR={135}^{\circ }and\angle PQT={110}^{\circ }$
$\angle SPR+\angle QPR={180}^{\circ }$ (Linear pair angles)
${135}^{\circ }+\angle QPR={180}^{\circ }$
$\therefore \angle QPR=180-135={45}^{\circ }$
Also, $\angle PQT+\angle PQR={180}^{\circ }$ (Linear pair angles)
$110+\angle PQR={180}^{\circ }$
$\therefore \angle PQR=180-110={70}^{\circ }$
As the sum of all interior angles of a triangle is ${180}^{\circ }$, in $\Delta PQR,$
$\angle QPR+\angle PQR+\angle PRQ={180}^{\circ }$
${45}^{\circ }+{70}^{\circ }+\angle PRQ={180}^{\circ }$
$\therefore \angle PRQ={180}^{\circ }-{115}^{\circ }$
i.e. $\angle PRQ={65}^{\circ }$