Two opposite angles of a parallelogram are $(3x- 2)^o$ and $(50 - x)^o$. Find the measure of each angle of the parallelogram.

Given:

Two opposite angles of a parallelogram are $(3x- 2)^o$ and $(50 - x)^o$.

To do:

We have to find the measure of each angle of the parallelogram.

Solution: 

We know that,

The opposite angles of a parallelogram are equal.

Adjacent angles of a parallelogram are supplementary.

Therefore,

$(3x-2)^o=(50-x)^o$

$3x+x=(50+2)^o$

$4x=(52)^o$

$x=\frac{52^o}{4}$

$x=13^o$

$\Rightarrow (3x-2)^o=[3(13)-2]^o=37^o$

Let the other two angles each be $y$.

This implies,

$(3x-2)^o+y=180^o$

$37^o+y=180^o$

$y=180^o-37^o$

$y=143^o$

The measure of each angle of the parallelogram is $37^o, 143^o, 37^o$ and $143^o$. 

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Updated on: 10-Oct-2022

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