If an angle is $28^o$ less than its complement, find its measure.


Given:

An angle is $28^o$ less than its complement.

To do:

We have to find the measure of the angle.

Solution:

An angle is said to be the complement of another angle if the sum of both the angles is $90^o$.

If $x$ is an angle, then its complement is $90^o - x$.

Let the required angle be $x$.

This implies,

Complement of angle $x=90^o-x$

According to the question,

$x=(90^o-x)-28^o$

$x=90^o-x-28^o$

$x+x=62^o$

$x=\frac{62^o}{2}$

$x=31^o$

Hence, the required angle is $31^o$.   

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Updated on: 10-Oct-2022

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