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

Question 1 Report

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

136

^{\circ}

124

^{\circ}

12

^{\circ}

68

^{\circ}

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 $^{\circ}$

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