SUPPLEMENTARY ANGLES

Two angles are supplementary, if they add up to 180⁰. 

Example :

120° and 60° are supplementary angles.

Because,

120° + 60° = 180°

Clearly, 120° is the supplement of 60° and 60° is the supplement of 120°.

Solved Problems

Problem 1 :

The measure of an angle is 108°. What is the measure of a supplementary angle?

Solution :

Let x be the measure of the required supplementary angle.

Because x and 108° are supplementary angles,

x + 108° = 180°

Subtract 108° from each side.

x = 72°

So, the measure of the supplementary angle is 72°.

Problem 2 :

The measure of an angle is 89°. What is the measure of a supplementary angle?

Solution :

Let x be the measure of the required supplementary angle.

Because x and 41° are supplementary angles,

x + 89° = 180°

Subtract 89° from each side.

x = 91°

So, the measure of the supplementary angle is 91°.

Problem 3 :

Find the value of  x :

Solution :

In the diagram shown above, the angles 

(2x + 3)° and (x - 6)°

are supplementary angles.

(2x +3)° + (x - 6)° = 180°

2x + 3 + x - 6  =  180

3x - 3  =  180

Add 3 to both sides. 

3x  =  183

Divide both sides by 3.

x  =  61

Problem 4 :

Find the value of  x :

Solution :

In the diagram shown above, the angles

(5x + 4)°, (x – 2)° and (3x + 7)°

are supplementary angles.

(5x + 4)° + (x – 2)° + (3x + 7)° = 180°

5x + 4 + x – 2 + 3x + 7 = 180

9x + 9 = 180

Subtract 9 from both sides.

9x = 171

Divide both sides by 9.

x = 19

Problem 5 :

Two angles are supplementary. If one angle is double the other angle, find the two angles.

Solution :

Let x be one of the angles.

Then the other angle is 2x.

Because x and 2x are supplementary angles,

x + 2x = 180°

3x = 180°

Divide both sides by 3.

x = 60°

2x = 2(60°) = 120°

So, the two angles are 60° and 120°.

Problem 6 :

Two angles are supplementary. If one angle is two times the sum of other angle and 3, find the two angles.

Solution :

Let x and y be the two angles which are supplementary.

x + y = 180° ----(1)

Given : One angle is two times the sum of other angle and 3.

x = 2(y + 3)

x = 2y + 6 ----(2)

Now, substitute (2y + 6) for x in (1). 

2y + 6 + y = 180

3y + 6 = 180

Subtract 6 from both sides. 

3y = 174

Divide both sides by 3.

y = 58

Substitute 58 for y in (2).

x = 2(58) + 6

x = 116 + 6

x = 122

So, the two angles are 122° and 58°.

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