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Question

Look at the figure given below. Can you find the measure of ∠y in the figure?

A

30

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B

60

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C

90

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D

120

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Solution

The correct option is A 30∘ Given: PQ = QR = RP = RS △PQR is an equilateral triangle because all sides are equal in length. Since we know that the sum of all the angles in a triangle is 180∘, Therefore, each angle measures 60∘. Now, using exterior angle property, ∠PQR + ∠QPR = ∠PSR=x ⇒x=60∘+60∘ ⇒x=120∘ In △ PRS, RS = PR (Given) ∴ △ PRS is an isosceles triangle. Using angle sum property, ∠PRS+∠RSP+∠SPR=180∘ ⇒x+y+y=180∘ ⇒x+2y=180∘ ⇒2y=180∘−120∘ ⇒2y=60∘ ⇒y=30∘

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