Question

In the given figure, PQ = PS and QR = RS. The measure of ZQPS is 230° and ZPQR is 25°. PS R S What is the measure of ZQRS?​

Answer 1

Answer:

Given, PQ⊥PS,PQ∥SR,∠SQR=28

∘

,∠QRT=65

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According to the question,

x+∠SQR=∠QRT (Alternate angles as QR is transversal.)

⇒x+28

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=65

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⇒x=37

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Also ∠QSR=x

⇒∠QSR=37

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Also ∠QRS+∠QRT=180

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(Linear pair)

⇒∠QRS+65

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=180

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⇒∠QRS=115

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Now, ∠P+∠Q+∠R+∠S=360

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(Sum of the angles in a quadrilateral.)

⇒90

∘

+65

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+115

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+∠S=360

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⇒270

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+y+∠QSR=360

∘

⇒270

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+y+37

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=360

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⇒307

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+y=360

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⇒y=53

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Answer 2

Answer:

Exterior angle = sum of two opposite interior angle

230°= 25+ x

x = 230 -25

x = 205

hence, < QRS = 205