If an angle differ from its complement by $10^o$, find the angle.

Given:

An angle differs from its complement by $10^o$.

To do:

We have to find the angle.

Solution:

Two angles are said to be complementary if the sum of their measures is $90^o$.

Let the required angle be $x$.

This implies,

The measure of the complementary angle is $x-10^o$ or $x+10^o$

Therefore,

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

$2x-10^o=90^o$ or $2x+10^o=90^o$

$2x=90^o+10^o$ or $2x=90^o-10^o$

$2x=100^o$ or $2x=80^o$

$x=\frac{100^o}{2}$ or $x=\frac{80^o}{2}$

$x=50^o$ or $x=40^o$

The measure of the required angle is $50^o$ or $40^o$.  

Tutorialspoint

Updated on: 10-Oct-2022

93 Views

Kickstart Your Career

Get certified by completing the course

Get Started