Related Angles - Supplementary Angles

definition

Supplementary angles: When the sum of the measures of two angles is 180° are called supplementary angles. Example, 60° + 120° = 180°.

Supplementary angles:

• When the sum of the measures of two angles is 180° are called supplementary angles.

• Example, 60° + 120° = 180°.

• The ‘60° angle’ is supplementary of the‘120° angle’ and vice versa.

• Acute angle is always lesser than 90º. It can be observed that two angles, even of 89º, cannot add up to 180º.
Therefore, two acute angles cannot be in a supplementary angle pair.

• Obtuse angle is always greater than 90º. It can be observed that two angles, even of 91º, will always add up to more than 180º.
Therefore, two obtuse angles cannot be in a supplementary angle pair.
• Right angles are of 90º and 90º + 90º = 180°.
Therefore, two right angles form a supplementary angle pair together.

Some more Examples,

Example

What will be the measure of the supplement of the following angles?

100º

Let the other measure of the angle is xº.

The sum of the measures of supplementary angles is 180º.

xº + 100º = 180º

xº = 180º - 100º

xº = 80º.

Example

What will be the measure of the supplement of the following angles?

55º

Let the other measure of the angle is xº.

The sum of the measures of supplementary angles is 55º.

xº + 55º = 180º

xº = 180º - 55º

xº = 125º.

Example

Among two supplementary angles, the measure of the larger angle is 44o more than the measure of the smaller. Find their measures.

Let the measure of larger angle be x° and the measure of smaller angle be y°.

Among two supplementary angles, the measure of the larger angle is 44° more than the measure of the smaller.

According to condition,

x = y + 44°

x + y = 180°

⇒ (y + 44°) + y = 180°

⇒ y + 44° + y = 180°

⇒ 2y + 44° = 180°

⇒ 2y = 180° - 44°

⇒ 2y = 136°

⇒ y = (136°)/2

⇒ y = 68°.

∴ x = y + 44°

x = 68° + 44°

x = 112°

Example

Find the measure of the supplement of an angle of 135°.

Let the supplementary angle measure p°.
The sum of the measures of two supplementary angles is 180°.
135 + p = 180
∴ 135 + p - 135 = 180 - 135
∴ p = 45
∴ The measure of the supplement of an angle of 135° is 45°.

Example

(a + 30)° and (2a)° are the measures of two supplementary angles. What is the measure of each angle?

a + 30 + 2a = 180
∴ 3a = 180 - 30
∴ 3a = 150
∴ a = 50
∴ a + 30 = 50 + 30 = 80°
∴ 2a = 2 × 50 = 100°
∴ The measures of the angles are 80° and 100°.

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What are Supplementary Angles? [00:10:15]
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