Question

If the complement of an angle is equal to the supplement of four times the angle,then find the measure of the angle.

Answer 1

Answer:

x=36

Step-by-step explanation:

Let one of the complementary angles be x

Now, the other angle is 90-x

Four times the angle = 4x

Supplement of 4 times the angle = 180-x

A.T.Q. ,

x=180-4x

-> 4x+x=180

-> 5x=180

-> x=180/5

After cancellation,

x=36

Answer 2

Given: The complement of an angle is equal to the supplement of four times the angle.

To find: The measure of the angle.

Solution:

• Two angles are said to be complementary to each other if their sum equals 90°.
• So, the complement of an angle is the difference between 90° and the angle.
• Two angles are said to be supplementary to each other if their sum equals 180°.
• So, the supplement of an angle is the difference between 180° and the angle.
• Let the angle to be measured be equal to x.
• According to the question, the equation obtained is as follows,

        $90 - x = 180 - 4x$

        $x = 30$

Therefore, the measure of the angle is 30°.