Question

If the supplement of an angle is two-thirds of itself. Determine the angle and its supplement.

Answer 1

The angle and its supplement are "108° and  72°".

Step-by-step explanation:

Let x be the angle and $\dfrac{2}{3} x$ be the its supplement.

To find, the angle and its supplement = ?

We know that,

The sum of supplementary angles = 180°

∴ x + $\dfrac{2}{3} x$ = 180°

⇒ $\dfrac{3x+2x}{3}$ = 180°

⇒ $\dfrac{5x}{3}$ = 180°

⇒ 5x = 180° × 3

⇒ 5x = 540°

⇒ x = $\dfrac{540}{5}$ = 108°

∴ Its supplement angle = $\dfrac{2}{3} \times 108$ =  2 × 36° = 72°

Thus, the angle and its supplement are "108° and  72°".