Question

Can two angles be supplementary if both of them are:

1. Acute?
2. Obtuse?
3. Right?

Answer 1

Step 1: According to definition of supplementary angles check whether two acute angles can be supplementary or not

An angle is said to be acute when the measure of the angle is less than $90°$

Hence, the sum of two acute angles$<90°+90°$

Hence, the sum of two acute angles is always less than $180°$

For a pair of angles to be supplementary, the sum of the angles must be equal to $180°$.

As the two acute angles cannot add up to $180°$ , two acute angles can not be supplementary.

Step 2: According to definition of supplementary angles check whether two obtuse angles can be supplementary or not:

An angle is said to be obtuse when the measure of the angle is more than $90°$

Hence, the sum of two obtuse angles$>90°+90°$

Hence, the sum of two obtuse angles is always more than $180°$

For a pair of angles to be supplementary, the sum of the angles must be equal to $180°$.

As the two obtuse angles add up to more than $180°$ , two obtuse angles can not be supplementary.

Step-3: According to definition of supplementary angles check whether two right angles can be supplementary or not

An angle is said to be a right angle when the measure of the angle is equal to $90°$

Hence, the sum of two right angles$=90°+90°=180°$

Hence, the sum of two right angles is always equal to$180°$

For a pair of angles to be supplementary, the sum of the angles must be equal to $180°$.

As the two right angles add up to exactly $180°$ , two right angles are always supplementary.