Question

an angle is two-thirds of its supplements find the angle​

Answer 1

Answer:

∠A = 72° , ∠B = 108°

Step-by-step explanation:

Let the angles be A & B.

Let ∠B = x -----> (1)

Given: ∠A = $\frac{2}{3} x$, ∠A + ∠B = 180°  ( supplementary angles )

∠A + ∠B = 180°  ( from given )

$\frac{2}{3}x$ + x = 180  ( substitute from (1) and given )

$\frac{2x + 3x}{3} = 180$  ( LCM of denominator )

$\frac{5x}{3} = 180$

5x = 180 × 3

5x = 540

x = $\frac{540}{5}$

∴ x = 108°

∠B = x ( from (1) )

∴ ∠B = 108°

∠A + ∠B = 180 ( from given )

∠A + 108 = 180

∠A = 180 - 108

∠A = 72°

   OR

∠A = $\frac{2}{3} x$  ( from given )

∠A =$\frac{2}{3} 108$

∠A = 2 × 36

∴ ∠A = 72°

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