Two adjacent angles of parallelogram are in the ratio $2:7$. Find the angles of parallelogram.

Given:

Two adjacent angles of parallelogram are in the ratio $2:7$.

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 $2x$ and $7x$.

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 $2x, 7x, 2x$ and $7x$.

$2x+7x+2x+7x=360^o$

$18x=360^o$

$x=\frac{360^o}{18}$

$x=20^o$

$\Rightarrow 2x=2(20^o)=40^o$

$\Rightarrow 7x=7(20^o)=140^o$

The measure of all the angles of the parallelogram is $40^o, 140^o, 40^o$ and $140^o$.

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Updated on: 10-Oct-2022

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