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