Question

Find the value of x in the given triangle

Answer 1

In ∆ABC, given B = 3x – 8°

∠XAZ = ∠BAC  ...[∵ vertically opposite angles]

8x + 7 + ∠BAC

i.e., In ∆ABC, ∠A = 8x + 7

Exterior angle ∠XCY = 120°

Exterior angle is equal to the sum of the interior opposite angles

∠A + ∠B = 120°

8x + 7 + 3x – 8 = 120°

8x + 3x = 120° + 8 – 7

11x = 121°

x = ${\displaystyle \frac{{121}^{\circ }}{11}}$

x = 11°