Two unequal angles of a parallelogram are in the ratio $2:3$. Find all its angles in degrees.

Given:

Two unequal angles of a parallelogram are in the ratio $2:3$.
To do:

We have to find all its angles in degrees.

Solution:

In ||gm ABCD,

Let $\angle A$ and $\angle B$ are unequal in a parallelogram $ABCD$.

This implies,

$\angle A : \angle B = 2 : 3$

Let $\angle A = 2x$

This implies,

$\angle B = 3x$

$\angle A + \angle B = 180^o$                  (Co interior angles are supplementary)

$2x + 3x = 180^o$

$5x = 180^o$

$x = \frac{180^o}{5}$

$x = 36^o$

Therefore,

$\angle A = 2x = 2(36^o) = 72^o$

$\angle B = 3x = 3(36^o) = 108^o$

Opposite angles are equal in a parallelogram.

Therefore,

$\angle C = \angle A = 72^o$

$\angle D = \angle B=108^o$

Hence, $\angle A = 72^o, \angle B = 108^o, \angle C = 72^o$ and $\angle D = 108^o$.

Tutorialspoint

Simply Easy Learning

Updated on: 10-Oct-2022

21 Views

Kickstart Your Career

Get certified by completing the course

Get Started