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

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

Explore More

Similar Questions

Show that the quadrilateral formed by joining the mid-points of the sides of a rhombus,taken in order,is a rectangle.

Difficult
View Solution

Prove that in a parallelogram,the bisectors of any two consecutive angles intersect at right angles.

Difficult
View Solution

In rhombus $ABCD$,$\angle A = \angle B - 30^{\circ}$,then $\angle C = \ldots$ (in $^{\circ}$)

$ABCD$ is a parallelogram and $P$ and $Q$ are points on the diagonal $AC$ such that $AP = PQ = QC$. Prove that $BQ \parallel DP$ and $BD$ bisects $PQ$.

If angles $A, B, C$ and $D$ of the quadrilateral $ABCD$,taken in order,are in the ratio $3:7:6:4$,then $ABCD$ is a

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