Question

Prove that supplement of an angle is an obtuse angle.

Answer 1

Prove that supplement of an angle is an obtuse angle.

1. We know that the two angles are supplementary angles if the sum of measures of those angles is equal to 180^o.
2. Obtuse angles are those which are greater than 90^o but less than 180^o.
3. The supplement of any angle can be found by subtracting the given angle from 180^o.

Let's take an obtuse angle $\theta$,

Then the supplement of $\theta$ will be ${(180-\theta )}^o$.

And we know that the ${90}^o<\theta <{180}^o$.

Therefore, ${90}^o<{(180-\theta )}^o<{180}^o$ (an obtuse angle)

Hence proved that the supplement of an angle is an obtuse angle.