Question

The supplement of an angle is four times the complement of the angle. Find the angle.
14. The ratio of an angle and its supplement is 5: 1. Find the angle.​

Answer 1

Solution ❶

Given :-

• The supplement of an angle is four times the complement of the angle.

To Find :-

• What is the angle.

Solution :-

• Let, the angle be x

• Supplement angle = 180° - x

• And, complement angle = 90° - x

According to the question,

⇒ (180° - x) = 4(90° - x)

⇒ 180° - x = 360° - 4x

⇒ - x + 4x = 360° - 180°

⇒ 3x = 180°

⇒ x = $\sf\dfrac{\cancel{180°}}{\cancel{3}}$

➠ x = 60°

∴ The angle is 60° .

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Solution ❷

Given :-

• The ratio of an angle and its supplement is 5:1.

To Find :-

• What is the angle.

Solution :-

• Let, the ratio be 5x : x

• And, the sum of supplement angle is 180°

According to the question,

⇒ 5x + x = 180°

⇒ 6x = 180°

⇒ x = $\sf\dfrac{\cancel{180°}}{\cancel{6}}$

➠ x = 30°

Hence, the required angles are,

➣ First angle = 5x = 5(30°) = 150°

➣ Second angle = x = 30°

Hope it helps!!

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