Question

In the given figure, if ΔEAT ~ ΔBUN, find the measure of all angles.

Answer 1

Given ΔEAT ≡ ΔBUN

∴ Corresponding angles are equal

∴ ∠E = ∠B  ...(1)

∠A = ∠U  ...(2)

∠T = ∠N  ...(3)

∠E = x°

∠A = 2x°

Sum of three angles of a triangle = 180°

In ΔEAT, x + 2x + ∠T = 180°

∠T = 180° – (x° + 2x°)

∠T = 180° – 3x°

Also in ΔBUN

(x + 40)° + x° + ∠U = 180°

x + 40° + x + ∠U = 180°

2x° + 40° + ∠U = 180°

∠U = 180° – 2x – 40° = 140° – 2x°

Now by (2)

∠A = ∠U

2x = 140° – 2x°

2x + 2x = 140°

4x = 140°

x = `140/4` = 35°

∠A = 2x° = 2 × 35° = 70°

∠N = x + 40° = 35° + 40° = 75°

∴ ∠T = ∠N = 75°

∠E = ∠B = 35°

∠A = ∠U = 70°