SUPPLEMENTARY ANGLES

Two angles are supplementary, if they add up to 90⁰. 

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°.

Practice 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 :

From the picture above, it is clear that (2x+3) and (x-6) are supplementary angles. 

Then,

(2x+3) + (x-6)  =  180

2x + 3 + x - 6  =  180

Simplify. 

3x - 3  =  180

Add 3 to each side. 

3x  =  183

Divide each side by 3. 

x  =  61

So, the value of x is 61.

Problem 4 :

Find the value of  x :

Solution :

From the picture above, it is clear (5x+4), (x-2) and (3x+7) are supplementary angles. 

Then, 

(5x+4) + (x-2) + (3x+7)  =  180

5x + 4 + x -2 + 3x + 7  =  180

Simplify. 

9x + 9  =  180

Subtract 9 from each side.

9x  =  171

Divide each side by 9.

x  =  19

So, the value of x is 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 each side by 3. 

x  =  60

And,

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.

So, we have

x + y  =  180° -----> (1)

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

Then, 

x  =  2(y + 3)

x  =  2y + 6 ----->(2)

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

(1)-----> 2y + 6 + y  =  180

3y + 6  =  180

Subtract 6 from each side. 

3y  =  174

Divide each side by 3.

y  =  58

Substitute 58 for y in (2).

(2)-----> x  =  2(58) + 6

x  =  116 + 6

x  =  122

So, the two angles are 122° and 58°.

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