20. Two supplementary angles are in the ratio $ 4: 5, $ find the smaller of the angles.
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Given: Two supplementary angles are in the ratio 4:5.

To find: We have to find the smallest of the two angles

Solution: 

Two angles are supplementary to each other when their sum is 180 degrees.

Now,

Given that angles are in ratio 4:5.

Let the common factor be = a.

So,

1^st angle = 4a

2^nd angle = 5a

Also,

4a + 5a = 180^o   

9a = 180^o   

a = $\frac{180^{0}}{9}$ 

a = 20^o  

Therefore, smaller angle is:

4a = 4 x 20^o = 80^o

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Updated on: 10-Oct-2022

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