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If an angle of a parallelogram is two-third of its adjacent angle, find the angles of the parallelogram.
Given:
An angle of a parallelogram is two-third of its adjacent angle.
To do:
We have to find the measure of each of the angles of the parallelogram.
Solution:
Let the measure of the adjacent angle be $3x$.
This implies,
The measure of the angle $=\frac{2}{3}\times3x=2x$.
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 $2x, 3x, 2x$ and $3x$.
$2x+3x+2x+3x=360^o$
$10x=360^o$
$x=\frac{360^o}{10}$
$x=36^o$
$\Rightarrow 2x=2(36^o)=72^o$
$\Rightarrow 3x=3(36^o)=108^o$
The measure of all the angles of the parallelogram is $72^o, 108^o, 72^o$ and $108^o$.