In this figure, PQ = PR = PS and SRT = 68∘ ∘ . Find QPS.

In this figure, PQ = PR = PS and SRT = 68${}^{\circ }$. Find QPS.

Answer Details

Since PQRS is quadrilateral 2y + 2x = QPS = 360${}^{\circ }$

i.e. 2(y + x) + QPS = 360${}^{\circ }$

QPS = 360${}^{\circ }$ - 2(y + x)

But x + y + 68${}^{\circ }$ = 180${}^{\circ }$

x + y = 180${}^{\circ }$ - 68${}^{\circ }$ = 180${}^{\circ }$

x + y = 180${}^{\circ }$ - 68${}^{\circ }$

= 112${}^{\circ }$

QPS = 360${}^{\circ }$ - 2(112${}^{\circ }$)

360${}^{\circ }$ - 224${}^{\circ }$ = 136${}^{\circ }$