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Question
In the given parallelogram YOUR, ∠RUO = 120° and OY is extended to point S such that ∠SRY = 50°. Find ∠YSR.
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Solution
Given, ∠RUO = 120° and ∠SRY = 50°
∠RYO = ∠RUO = 120° ...[∵ Opposite angles of a parallelogram]
Now, ∠SYR = 180° – ∠RYO ...[Linear pair]
= 180° – 120°
= 60°
In ΔSRY,
By the angle sum property of a triangle,
∠SRY + ∠RYS + ∠YSR = 180°
⇒ 50° + 60° + ∠YSR = 180°
⇒ ∠YSR = 180° – (50° + 60°)
⇒ ∠YSR = 180° – 110°
∴ ∠YSR = 70°
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