An angle of more than $90^°$ but less than $180^°$ is called an obtuse angle.

The meaning of an obtuse angle is, the angle of greater than $90^\circ$ and less than $180^\circ$. So, an angle which lies between $90^\circ$ and $180^\circ$ is called an obtuse angle.

So, the range of an obtuse angle can be written as $(90^\circ, 180^\circ)$ in mathematics.

In geometric system, obtuse angles are formed in two possible ways.

1

The angle of a line is measured from zero degrees line. If a line makes an angle more than $90^\circ$ and less than $180^\circ$ with surface of the earth, the angle is called as an obtuse angle.

$\overrightarrow{OP}$ is a ray and it is at zero angle at its initial position.

The same ray is rotated an angle of $123^\circ$ in anticlockwise direction to reach its final position where the ray $\overrightarrow{OP}$ is become $\overrightarrow{OQ}$.

The ray is made an angle of $123^\circ$ from its initial position to final position.

$\angle QOP = 123^\circ$

The angle $QOP$ is more than $90^\circ$ but less than $180^\circ$. Hence, the angle made by the ray $\overrightarrow{OP}$ to reach from its initial position to final position is an example to an obtuse angle.

2

The angle between any two lines which have a common vertex is measured by considering one line as baseline to another and vice-versa to measure the angle. If the angle between them is greater than $90^\circ$ and less than $180^\circ$, the angle is called as an obtuse angle in geometric system.

$\overrightarrow{RS}$ and $\overrightarrow{RT}$ are two rays and they both are started travelling from a point $R$.

The two rays $\overrightarrow{RS}$ and $\overrightarrow{RT}$ continued travelling infinitely from point $R$. The angle between them is measured by taking one line as baseline to another line and vice-versa.

The angle between the rays $\overrightarrow{RS}$ and $\overrightarrow{RT}$ is measured as $165^\circ$ angle.

$\angle SRT = 165^\circ$

The angle $SRT$ is more is greater than $90^\circ$ but less than $180^\circ$. Therefore, the angle between rays $\overrightarrow{RS}$ and $\overrightarrow{RT}$ is an example for an obtuse angle.

Latest Math Topics

Jan 06, 2023

Jan 03, 2023

Jan 01, 2023

Dec 26, 2022

Dec 08, 2022

Latest Math Problems

Nov 25, 2022

Nov 02, 2022

Oct 26, 2022

Oct 24, 2022

Sep 30, 2022

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

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

Learn how to solve the maths problems in different methods with understandable steps.

Copyright © 2012 - 2022 Math Doubts, All Rights Reserved