The measures of two adjacent angles of a parallelogram are in the ratio 3:2. Find the measure of each of the angles of the parallelogram.

Given:

The measures of two adjacent angles of a parallelogram are in the ratio 3:2.

To do:

We have to find the measure of each of the angles of the parallelogram.
Solution:
 Let the two adjacent angles of the parallelogram be $3x$ and $2x$.

We know that,

Sum of the angles in a parallelogram is $360^o$ and opposite angles of a parallelogram are equal.

Therefore,

The four angles of the parallelogram are $3x, 2x, 3x$ and $2x$.

$3x+2x+3x+2x=360^o$

$10x=360^o$

$x=\frac{360^o}{10}$

$x=36^o$

$\Rightarrow 3x=3(36^o)=108^o$

$\Rightarrow 2x=2(36^o)=72^o$

The measure of all the angles of the parallelogram is $108^o, 72^o, 108^o$ and $72^o$.

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Updated on: 10-Oct-2022

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