Question

In the figure, If PQ I to PS and PQ||SR. ZSQR = 28º and QRT = 65°. then find the
values of x and y.
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Answer 1

Correct Question :

If PQ is perpendicular to PS , PQ // SR , ∠SQR = 28° and ∠QRT = 65° , the find the values of x and y .

Given :

• PQ is perpendicular to PS .
• PQ // SR
• ∠SQR = 28°
• ∠QRT = 65°

To Find :

• Values of x and y .

Solution :

$\longmapsto\tt{\angle{PQR}=\angle{QRT}\:(Alternate\:Angles)}$

$\longmapsto\tt{x+28^{\circ}=65^{\circ}}$

$\longmapsto\tt{x=65^{\circ}-28^{\circ}}$

$\longmapsto\tt\bf{x=37^{\circ}}$

In Δ PQS :

$\longmapsto\tt{\angle{PQS}+\angle{PSQ}+\angle{QPS}=180^{\circ}\:(A.S.P)}$

$\longmapsto\tt{37^{\circ}+y+90^{\circ}=180^{\circ}}$

$\longmapsto\tt{y+127^{\circ}=180^{\circ}}$

$\longmapsto\tt{y=180^{\circ}-127^{\circ}}$

$\longmapsto\tt\bf{y=53^{\circ}}$

Therefore :

$\longmapsto\tt\bf{Value\:of\:x=37^{\circ}}$

$\longmapsto\tt\bf{Value\:of\:y=53^{\circ}}$