Question

In figure 6, if PQ ⊥ PS, PQ ∥ SR, ∠SQR = 28 0 and ∠QRT = 65 0 then find the values of x and y.​

Answer 1

Step-by-step explanation:

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∘