Question

find the measure of an angle which is 24 degree more than its complement

Answer 1

Let the angle be x

Then its complement angle will be (x-24)

Sum of angles = 90

=> x + (x-24) = 90

=> 2x - 24 = 90

=> 2x = 90 + 24

=> 2x = 114

=> x = 114/2 = 57°

The angle which is 24° more than its complement angle is 57°.

Answer 2

Given:

The angle more than its complement is = 24°

To Find:

The angle is 24° more than its complement.

Solution:

For Finding that angle,

Let us assume the angle to be '$x$'.

According to the question,

The complement of the assumed angle given is 24° less than the angle,

                                              $=x-24$

By Using the complement angle property,

The sum of the actual and the complement angle is equal to 90°.

                      $Sum~of~angles=90\\~~~~~x+(x-24)=90\\~~~~~~~~~~~~~~~~~~2x=90+24\\~~~~~~~~~~~~~~~~~~~~x=\frac{114}{2}\\~~~~~~~~~~~~~~~~~~~~x=57$

Hence the 57° angle is 24° more than its complement angle.