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Question
Find the values of x and y in the given figure.
Solution
In ΔTQS, ∠T + ∠Q + ∠S = 180° ......[Angle sum property of a triangle]
⇒ 50° + 30° + ∠1 = 180°
⇒ 80° + ∠1 = 180°
⇒ ∠1 = 180° – 80° = 100°
Now, ∠1 + x = 180° ......[Linear pair]
⇒ 100° + x = 180° = 180° – 100°
⇒ x = 80°
In ΔTSR, x + 45° + ∠2 = 180° ......[Angle sum property of a triangle]
⇒ ∠2 = 180° – 80° – 45° = 55°
Now, 50° + ∠2 + y = 180°
⇒ 50° + ∠2 + y = 180° ......[Linear pair]
y = 180° – 50° – 55° = 75°
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