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Supplementary Angles

Definition of Supplementary Angles

Two angles are mentioned to be supplementary if the sum of their measures is 180°. Every angle is the complement of the opposite.

Examples of Supplementary Angles

The next pairs of angles are supplementary. Every pair of angles provides as much as 180°.

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

• When two strains intersect, forming 4 angles, the adjoining angles are all the time supplementary. (Adjoining angles are two angles which can be subsequent to one another.)

• Supplementary angles kind a straight angle when adjoining. (A straight angle has a measure of 180°. Straight angle varieties a straight line.)

Solved Examples on Supplementary Angles

Instance 1
If the measure of an angle is 59 levels, what’s the measure of its complement?

Resolution:
Let’s name the complement ‘x’.
“Two angles are mentioned to be supplementary if the sum of their measures is 180°.”

So:
59° + x = 180°

Subtract 59 from both sides.
59° + x – 59° = 180° – 59°
x = 121°
So, the complement of 59 levels is 121 levels.

Instance 2
Angles A and B are supplementary. If the measure of angle A equals the measure of angle B, then discover the measures of angles A and B.

Resolution:
On condition 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 mentioned to be supplementary if the sum of their measures is 180°.”

So:
x + x = 180°

Simplify
2x = 180°

Divide both sides by 2.
2x/2 = 180°/2
x = 90°

Due to this fact the measure of every angle is 90°.

Instance three
Two angles are supplementary. The angle measures are within the ratio 5:7. Discover the measure of every angle.

Resolution:
The angle measures are within the ratio 5:7.
So, the angle measures could be represented by 5x and 7x.

The 2 angles are supplementary.
“Two angles are mentioned to be supplementary if the sum of their measures is 180°.”

So:
5x + 7x = 180°

Simplify.
12x = 180°

Divide both sides by 12.
12x/12 = 180°/12
x = 15°

Due to this fact the angle measures are 5x = 5 × 15° = 75° and 7x = 7 × 15° = 105°.

Instance four
Two angles are supplementary. The bigger angle is 15 levels greater than twice the smaller angle. What are the measures of the angles?

Resolution:
On condition that the bigger angle is 15 levels greater than twice the smaller angle.
Let ‘x’ symbolize the measure of the smaller angle.

Then:

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

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

So:
Measure of bigger angle + measure of smaller angle = 180°
(2x + 15°) + x = 180°

Simplify.
3x + 15° = 180°

Subtract 15 from both sides.
3x + 15° – 15° = 180° – 15°
3x = 165°

Divide both sides by three.
3x/three = 165°/three
x = 55°

Due to this fact the measure of the smaller angle is x = 55° and the measure of the bigger angle is 2x + 15° = 2 × 55° + 15° = 110° + 15° = 125°. Author:Navid

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