Math Doubts

Complementary angles

Complementary angles

The angles whose sum equals to $90^\circ$ are called the complementary angles.


Complementary angles are angles basically but the sum of them represents a right angle when the angles are added to each other.

One angle is known as complement of another angle and vice-versa.


Complementary angles

$\alpha$ and $\beta$ are two angles. The sum of them forms a right angle geometrically.

$\alpha+\beta = 90^\circ$

  1. $\alpha$ is called complement of $\beta$
  2. $\beta$ is called complement of $\alpha$

The angles $\alpha$ and $\beta$ are known as complementary angles.


Complementary angles example

$\Delta MON$ is a right triangle.

It has three interior angles. One angle ($\angle OMN$) is right angle. The other two angles are $\angle MNO$ and $\angle NOM$.

The $\angle MNO$ is $55^\circ$ and the $\angle NOM$ is $35^\circ$. Now, add both angles.

$\angle MNO + \angle NOM$ $=$ $55^\circ + 35^\circ$

$\implies$ $\angle MNO + \angle NOM$ $=$ $90^\circ$

The sum of two angles is right angle $\Big(\dfrac{\pi}{2}\Big)$. Therefore, the angles ($\angle MNO$ and $\angle NOM$) are called as complementary angles.

The $\angle MNO$ is called as complement of the $\angle NOM$. Similarly, $\angle NOM$ is called as complement of the $\angle MNO$.

Math Doubts
Math Doubts is a free math tutor for helping students to learn mathematics online from basics to advanced scientific level for teachers to improve their teaching skill and for researchers to share their research projects. Know more
Follow us on Social Media
Math Problems

Learn how to solve easy to difficult mathematics problems of all topics in various methods with step by step process and also maths questions for practising.

Learn more