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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 $\angle D = 108^o$.
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