An angle is $ 10^{\circ} $ more than its complement, find the angle.

Given:

An angle is \( 10^{\circ} \) more 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,

$x=(90^o-x)+10^o$

$x=90^o-x+10^o$

$x+x=100^o$

$x=\frac{100^o}{2}$

$x=50^o$

Hence, the required angle is $50^o$.