Among two supplementary angles, the measure of the larger angle is 44^o more than the measure of the smaller. Find their measures.

Given: Among two supplementary angles, the measure of the larger angle Is $44^{o}$ more than the measure of the smaller.

To find: Here we have to find the measure of the angles.

Solution:

Let the smaller angle be $=\ a$

So, the larger angle be $=\ a\ +\ 44^{o}$

Now,

Two angles are supplementary to each other when their sum is $180^{o}$. Therefore,

$a\ +\ (a\ +\ 44^{o})\ =\ 180^{o}$  

$2a\ =\ 180^{o}\ -\ 44^{o}$  

$2a\ =\ 136^{o}$   

$a\ =\ \frac{136^{o}}{2}$  

$a\ =\ 68^{o}$   

So,

The smaller angle be $=\ a\ =\ \mathbf{68^{o}}$

And,

The larger angle be $=\ a\ +\ 44^{o}\ =\ 68^{o}\ +\ 44^{o}\ =\ \mathbf{112^{o}}$  

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Updated on: 10-Oct-2022

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