The supplement of an acute angle is ________ . - Vidyadip

Question

The supplement of an acute angle is ________ .

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Answer

The supplement of an acute angle is an obtuse angle.
Explanation:
As the sum of the supplementary angles is180°.
Let one of the angle measure x°, such that x < 90.
Let the other angle measures y°.
As the angles are supplementary there sum is 180°.
x + y = 180° ...(1)
x < 90° ...(2)
Now subtracting (1) from (2)
-y < -90°
y > 90°
Then, other angle y is clearly an obtuse angle.
Illustration:
Let the given acute angle be 30°
Then, the other angle becomes
(180 - 30)° = 150°
This is clearly an obtuse angle.

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