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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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