Math Doubts

Obtuse angle

obtuse angle


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.

Case study

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


Obtuse angle by a Line

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.

obtuse angle by the rotation of a line

$\overrightarrow{OP}$ 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.


Obtuse angle between two lines

obtuse angle between two lines

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.

Math Questions

The math problems with solutions to learn how to solve a problem.

Learn solutions

Math Worksheets

The math worksheets with answers for your practice with examples.

Practice now

Math Videos

The math videos tutorials with visual graphics to learn every concept.

Watch now

Subscribe us

Get the latest math updates from the Math Doubts by subscribing us.

Learn more

Math Doubts

A free math education service for students to learn every math concept easily, for teachers to teach mathematics understandably and for mathematicians to share their maths researching projects.

Copyright © 2012 - 2023 Math Doubts, All Rights Reserved