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

"

** 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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