Question

The supplement of an acute angle is .................

Answer 1

The supplement of an acute angle is an obtuse angle.

Explanation:

As the sum of the supplementary angles is 180°.

Let one of the angle measures 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 subracting (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.