Question

In the following figure, if ST = SU, then find the values of x and y.

Answer 1

Given, ST = SU

∴ ∠SUT = ∠STU = y  ...[∵ Angles opposite to equal sides are equal]

Also, ∠1 = 78°  ...[Vertically opposite angles]

In ΔSUT, 78° + y + y = 180°  ...[Angle sum property of a triangle]

⇒ 78° + 2y = 180°

⇒ 2y = 180° – 78° = 102°

⇒ y = `102^circ/2` = 51°

Also, x + y = 180°  ...[Linear pair]

⇒ x + 51° = 180°

⇒ x = 180° – 51°

⇒ x = 129°