Can all the angles of a quadrilateral be acute angles? Give reason for your answer.

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(N/A) No,all the angles of a quadrilateral cannot be acute angles.
An acute angle is defined as an angle less than $90^{\circ}$.
If all four angles of a quadrilateral were acute,each angle would be less than $90^{\circ}$.
Consequently,the sum of these four angles would be less than $90^{\circ} + 90^{\circ} + 90^{\circ} + 90^{\circ} = 360^{\circ}$.
However,the sum of the interior angles of a quadrilateral is always exactly $360^{\circ}$.
Therefore,it is impossible for all four angles to be acute.

Explore More

Similar Questions

All the angles of a quadrilateral are equal. What special name is given to this quadrilateral?

$ABCD$ is a rhombus such that $\angle ACB = 40^{\circ}$. Then $\angle ADB$ is (in $^{\circ}$)

$PQ$ and $RS$ are two equal and parallel line segments. Any point $M$ not lying on $PQ$ or $RS$ is joined to $Q$ and $S$. Lines are drawn through $P$ parallel to $QM$ and through $R$ parallel to $SM$,meeting at $N$. Prove that line segments $MN$ and $PQ$ are equal and parallel to each other.

Difficult
View Solution

In trapezium $ABCD$,$AB \parallel CD$. If $\angle A = 70^{\circ}$ and $\angle B = 85^{\circ}$,then $\angle D = \ldots$ (in $^{\circ}$)

Diagonals of a rhombus are equal and perpendicular to each other. Is this statement true? Give reason for your answer.

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo