Question

an angle is 1/5 th of its complement. find the angles

Answer 1

The angle is 15° and its complementary angle is 75°

Given :

An angle is 1/5 th of its complement

To find :

The angles

Solution :

Step 1 of 2 :

Form the equation to find the angles

Here it is given that an angle is 1/5 th of its complement

Let the angle = x

We know that two angles are said to be complementary if sum of the angles is 90°

So complementary angle of x = 90° - x

By the given condition

x = 1/5(90° - x)

Step 2 of 2 :

Find the angles

x = 1/5(90° - x)

⇒ 5x = 90° - x

⇒ 6x = 90°

⇒ x = 90°/6

⇒ x = 15°

∴ The measure of the angle = 15°

∴ The measure of its complementary angle

= 90° - 15°

= 75°

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