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Q.

Among two supplementary angles, the measure of the larger angle is 36° more than the measure of the smaller. The measure of the smaller angle is ____°.

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Detailed Solution

Among two supplementary angles, the measure of the larger angle is 36° more than the measure of the smaller. The measure of the smaller angle is 72°.
Given among two supplementary angles, the measure of the larger angle is 36° more than the measure of the smaller.
Let the larger angle = x.
As the angle is supplementary, therefore, the other angle is 180 – x.
Now according to the question,

180 − x ° + 36 ° = x °

216 = 2 x

x = 108

The larger angle = 108°.
Now smaller angle is,
= 108 – 36
= 72

∘

The smaller angle is 72°.

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