Question

`In the given figure, if PQ∥RS,∠QR= 112^{°} and x:y=5:3 then which of thefollowing options is correct?P Qx 112^{°} QπyR s`​

Answer 1

Answer:

Solution



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Given, PQ⊥PS,PQ∥SR,∠SQR=28∘,∠QRT=65∘

According to the question,

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

⇒x+28∘=65∘

⇒x=37∘

Also ∠QSR=x

⇒∠QSR=37∘

Also ∠QRS+∠QRT=180∘ (Linear pair)

⇒∠QRS+65∘=180∘

⇒∠QRS=115∘

Now, ∠P+∠Q+∠R+∠S=360∘ (Sum of the angles in a quadrilateral.)

⇒90∘+65∘+115∘+∠S=360∘ 

⇒270∘+y+∠QSR=360∘

⇒270∘+y+37∘=360∘ 

⇒307