Question

If the ratio of the complementary angle and the supplementary angle of an angle ∠A is 1∶4, then find ∠A. PLEASE HELP ME AND ANSWER AS QUICKLY AS U CAN

Answer 1

The complementary angle and the supplementary angle of an angle ∠A is 1∶4. Then, ∠A = 60°

Explanation:

Let the required angle be x

Then according to the question,

⇒  ( 90° − x ) /   ( 180° − x )  = 1/4

⇒  4(90° −x) = 180°−x

⇒  360°−4x = 180°−x

⇒  360°−180° = −x+4x

⇒  180° = 3x

⇒  x = 3/180°

Therefore  x = 60°

Therefore  the required angle is 60°.

Answer 2

Step-by-step explanation:

Given that:The ratio of the complementary angle and the supplementary angle of an angle ∠A is 1∶4.

To find: ∠A

Solution: We know that

two angles are said to be complementary if sum of both are 90° and supplementary if sum of both are 180°.

Thus, complement of ∠A = 90°-∠A

supplements of ∠A = 180°-∠A

$\frac{90° - \angle A}{180° - \angle A} = \frac{1}{4} \\ \\ 360° - 4\angle A = 180° - \angle A \\ \\ - 4\angle A+ \angle A = 180 - 360° \\ \\ - 3\angle A = - 180° \\ \\ \angle A = \frac{180°}{3} \\ \\ \blue{\bold{\angle A = 60°}}$

Thus, ∠A is 60°.

Hope it helps you.