Question

In the adjoining finger,QP Perpendicular PS, PQ parallel SR, angle SQR=28 degree and angle QRT=65 degree, find x and y

Answer 1

Hello mate ☺

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Solution-

It is given that PQ∥SR. Therefore, ∠QRT=∠PQR              (Alternate Interior Angles)

⇒65°=x+28°

⇒x=65°−28°=37°

In ∆PQS, we have

x+y+∠SPQ=180°       (Sum of three angles of a triangle =180°)

⇒37°+y+90°=180°        ( It is given that ∠SPQ=90°)

⇒y=180°-37°−90°=53°

Therefore, x=37° and y=53°

I hope, this will help you.☺

Thank you______❤

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Answer 2

Solutions:

Since PQ || SR and QR is a transversal.

Hence, ∠PQR = ∠TRQ ............. [Alternate angles]

=> X + 28° = 65°

=> X = 37°

Using angle sum property in △PQS, we obtain

=> ∠QPS + ∠PQS + ∠PSQ = 180°

=> 90° + 37° + Y = 180°

=> 127° + Y = 180°

=> Y = 53°