Supplementary Angles

Definition of Supplementary Angles

Two angles are said to be supplementary if the sum of their measures is 180°. Each angle is the supplement of the other.

Examples of Supplementary Angles

The following pairs of angles are supplementary. Each pair of angles adds up to 180°.

15°, 165°
45°, 135°
20°, 160°
72°, 108°
83°, 97°

More about Supplementary Angles

• When two lines intersect, forming four angles, the adjacent angles are always supplementary. (Adjacent angles are two angles that are next to each other.)

• Supplementary angles form a straight angle when adjacent. (A straight angle has a measure of 180°. Straight angle forms a straight line.)

Solved Examples on Supplementary Angles

Example 1

If the measure of an angle is 59 degrees, what is the measure of its supplement?

Solution:

Let’s call the supplement ‘x’.

“Two angles are said to be supplementary if the sum of their measures is 180°.”

So:

59° + x = 180°

Subtract 59 from each side.

59° + x – 59° = 180° – 59°
x = 121°

So, the supplement of 59 degrees is 121 degrees.


Example 2

Angles A and B are supplementary. If the measure of angle A equals the measure of angle B, then find the measures of angles A and B.

Solution:

Given that the measure of angle A equals the measure of angle B.
Let measure of angle A = measure of angle B = x.

Angles A and B are supplementary.

“Two angles are said to be supplementary if the sum of their measures is 180°.”

So:

x + x = 180°

Simplify

2x = 180°

Divide each side by 2.

2x/2 = 180°/2
x = 90°

Therefore the measure of each angle is 90°.


Example 3

Two angles are supplementary. The angle measures are in the ratio 5:7. Find the measure of each angle.

Solution:

The angle measures are in the ratio 5:7.
So, the angle measures can be represented by 5x and 7x.

The two angles are supplementary.
“Two angles are said to be supplementary if the sum of their measures is 180°.”

So:

5x + 7x = 180°

Simplify.

12x = 180°

Divide each side by 12.

12x/12 = 180°/12
x = 15°

Therefore the angle measures are 5x = 5 × 15° = 75° and 7x = 7 × 15° = 105°.


Example 4

Two angles are supplementary. The larger angle is 15 degrees more than twice the smaller angle. What are the measures of the angles?

Solution:

Given that the larger angle is 15 degrees more than twice the smaller angle.
Let ‘x’ represent the measure of the smaller angle.

Then:

Measure of the larger angle = twice the smaller angle + 15° = 2 × x + 15° = 2x + 15°
The two angles are supplementary.

“Two angles are said to be supplementary if the sum of their measures is 180°.”

So:

Measure of larger angle + measure of smaller angle = 180°

(2x + 15°) + x = 180°

Simplify.

3x + 15° = 180°

Subtract 15 from each side.

3x + 15° – 15° = 180° – 15°
3x = 165°

Divide each side by 3.

3x/3 = 165°/3
x = 55°

Therefore the measure of the smaller angle is x = 55° and the measure of the larger angle is 2x + 15° = 2 × 55° + 15° = 110° + 15° = 125°.



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I’m Chandrajeet, an in-house writer for iCoachMath. iCoachMath is an effective, convenient, easy-to-use online Math Program which has been used by thousands of students, teachers, and parents.iCoachMath strives to lead K-12 students to excellence in math by offering quality web-based educational solutions. iCoachMath’s instructional and lesson materials are aligned to State Curriculum Standards in all 50 states (USA).
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