Question

Find the values of x and y in the following figure.

Answer 1

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°