Question

In the given figure, if PQ 1 PS, PQ || SR, Z SQR = 28 ° and Z QRT = 65 °, then find the values​

Answer 1

Answer:

In △QSR, we have 

∠QRT=∠RSQ+∠SQR     ....(Exterior angle of triangle is equal t sum of interior opposite angles)

⇒65∘=∠RSQ+28∘

⇒∠RSQ=65∘−28∘

⇒∠RSQ=37∘

We have y∘+∠RSQ=90∘    ....(Given)

⇒y+37∘=90∘

⇒y=90∘−37∘=53∘

In △PQS, we have

x∘+y∘+∠P=180∘     ....(Angle sum property)

⇒x+53∘+90∘=180∘

⇒x=180∘−143∘=37∘

Answer 2

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Answer:

In △QSR, we have 

∠QRT=∠RSQ+∠SQR     ....(Exterior angle of triangle is equal t sum of interior opposite angles)

⇒65∘=∠RSQ+28∘

⇒∠RSQ=65∘−28∘

⇒∠RSQ=37∘

We have y∘+∠RSQ=90∘    ....(Given)

⇒y+37∘=90∘

⇒y=90∘−37∘=53∘

In △PQS, we have

x∘+y∘+∠P=180∘     ....(Angle sum property)

⇒x+53∘+90∘=180∘

⇒x=180∘−143∘=37∘