In the given figure, if ∆EAT ~ ∆BUN find the measure of all angles

1.	In the given figure, if ∆EAT ~ ∆BUN find the measure of all angles.
Answer» Given ∆EAT ≡ ∆BUN ∴ 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 ∆EAT, x + 2x + ∠T = 180° ∠T = 180° – (x° + 2x° ) ∠T = 180°- 3x° …(4) Also in ∆BUN (x + 40)° + + ∠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°

In the given figure, if ∆EAT ~ ∆BUN find the measure of all angles.

Answer»

Given ∆EAT ≡ ∆BUN

∴ 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 ∆EAT, x + 2x + ∠T = 180°

∠T = 180° – (x° + 2x° )

∠T = 180°- 3x° …(4)

Also in ∆BUN

(x + 40)° + + ∠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°