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Question
In the figure given below, if RS is parallel to PQ, then find the value of ∠y.
Solution
In ΔPQR,
∠P + ∠Q + ∠R = 180° ....(angle sum property)
⇒ 4x° + 5x° + 9x° = 180°
⇒ 18x° = 180°
⇒ x = 10
⇒ ∠P = 4x° = 4 x 10° = 40°
∠Q = 5x° = 5 x 10° = 50°
∠QPR = ∠PRS ....(Alternate angles)
And, ∠QPR = 40°
∠PRS = 40°
By exterior angle property,
∠PQR + ∠QPR = ∠PRS + y°
⇒ 40° + 50° = 40° + y°
⇒ y = 50°
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