Math Doubts

Supplementary angles

supplementary angles

The angles whose sum equals to $180^\circ$ are called the supplementary angles.

Introduction

Supplementary angles are basically two angles but the sum of them represents a straight angle when the angles are added to each other.

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

Formula

supplementary angles

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

$\alpha+\beta = 180^\circ$

  1. $\alpha$ is called as supplement of $\beta$
  2. $\beta$ is called as supplement of $\alpha$

The two angles $\alpha$ and $\beta$ are known as supplementary angles.

Example

$\Delta PQR$ is a triangle and the side $\overline{RS}$ splits this triangle as two triangles $\Delta PSR$ and $\Delta QSR$.

supplementary angles example

Measures $\angle PSR$ and $\angle QSR$ by using protractor.

It is measured that the $\angle PSR$ is equal to $48^\circ$ and the $\angle QSR$ is equal to $132^\circ$. Now, add both angles to get sum of them.

$\angle PSR + \angle QSR$ $=$ $48^° + 132^°$

$\implies$ $\angle PSR + \angle QSR$ $=$ $180^°$

The sum of the two angles is straight angle ${(\pi)}$. Therefore, the angles ($\angle PSR$ and $\angle QSR$) are called as supplementary angles.

The $\angle PSR$ is called as supplement of the $\angle QSR$. Similarly, $\angle QSR$ is called as supplement of the $\angle PSR$.

Math Doubts

A best free mathematics education website that helps students, teachers and researchers.

Maths Topics

Learn each topic of the mathematics easily with understandable proofs and visual animation graphics.

Maths Problems

A math help place with list of solved problems with answers and worksheets on every concept for your practice.

Learn solutions

Subscribe us

You can get the latest updates from us by following to our official page of Math Doubts in one of your favourite social media sites.

Copyright © 2012 - 2022 Math Doubts, All Rights Reserved