SOLVING COMPLEMENTARY AND SUPPLEMENTARY WORD PROBLEMS

Problem 1 :

Angles G and H are complementary. If m∠G = 3x + 6 and m∠H = 2x - 11. what is the measure of each angle?

Solution :

Complementary angles measure 90˚.

∠G + ∠H = 90˚

3x + 6 + 2x - 11 = 90˚

5x - 5 = 90˚

5x = 95

x = 19

So,

m∠G = 3x + 6

m∠G = 3(19) + 6

 = 57 + 6

m∠G = 63˚

m∠H = 2x - 11

 = 2(19) - 11

 = 38 - 11

m∠H = 27˚

So, the measure of angles are m∠G = 63˚ and m∠H = 27˚.

Problem 2 :

The measures of angles A and B are supplementary. What is the measure of each angle?

Solution:

Supplementary angles measure 180˚.

 m∠A+ m∠B = 180˚

For example,

Let m∠A = 60˚

60 + m∠B = 180˚

m∠B = 180˚ - 60˚

m∠B = 120˚

So, the measure of angles are m∠A = 60˚ and m∠B = 120˚

Problem 3 :

An angle is five its supplement. Find both angles.

Solution:

The two angles x and y are to be supplementary angles.

x + y = 180˚

Then,

x = 5y

5y + y = 180˚

6y = 180˚

y = 30˚

Therefore, 

x = 5(30˚)

x = 150˚

So, both angles are 150˚ and 30˚.

Problem 4 :

An angle is 74 degrees more than its complement. Find both angles.

Solution:

Complementary angles measure 90˚.

Let one angle = x

Complementary angle = x + 74

x + x + 74 = 90˚

2x + 74 = 90˚

2x = 90 - 74

2x = 16

x = 8˚

So,

one angle = 8˚

Second angle = x + 74

= 8 + 74

= 82˚

So, both angles are 8˚ and 82˚.

Problem 5 :

The supplement of an angle exceeds the angle by 60 degrees. Find both angles.

Solution: 

The two angles x and y are to be supplementary angles.

x + y = 180˚

Let one angle is x and second angle is x + 60˚

x + x + 60 = 180˚

2x + 60 = 180

2x = 180 - 60

2x = 120

x = 60

Second angle = x + 60˚

= 60 + 60

= 120˚

So, both angles are 60˚ and 120˚.

Problem 6 :

Find the number of degrees in an angle which is 42 less than its complement.

Solution:

Complementary angles measure 90˚.

Let the angle be x.

Complementary angle = 90˚ - x

x = (90 - x) - 42

x = 48 - x

2x = 48

x = 24

So,

First angle = 24˚ 

Second angle = 90 - x

= 90 - 24

= 66˚

Problem 7 :

Find the number of degrees in an angle which is 120 less than its supplement.         

Solution:

Let the angle be x.

Supplementary angle = 180˚ - x

x = (180 - x) - 120

x = 60 - x

2x = 60

x = 30

So,

First angle = 30˚ 

Second angle = 180 - x

= 180 - 30

= 150˚

Problem 8 :

The complement of an angle is 30 less than twice the angle. Find the larger angle.

Solution:

Let the angle be x.

Complementary angle = 90˚ - x

90 - x = 2x - 30

90 + 30 = 2x + x

3x = 120

x = 40

So, 

First angle = 40˚

Second angle = 90˚ - x

= 90 - 40

= 50˚

Problem 9 :

Angles A and B are complementary. If m∠A = 3x - 8 and m∠B = 5x + 10, what is the measure of each angle?

Solution:

Complementary angles measure 90˚.

∠A + ∠B = 90˚

3x - 8 + 5x + 10 = 90˚

8x + 2 = 90˚

8x = 88

x = 11

So,

m∠A = 3x - 8

m∠A = 3(11) - 8

 = 33 - 8

m∠A = 25˚

m∠B = 5x + 10

 = 5(11) + 10

 = 55 + 10

m∠B = 65˚

So, the measure of angles are m∠A = 25˚ and m∠B = 65˚.

Problem 10 :

Angles Q and R are supplementary. If m∠Q = 4x + 9 and m∠R = 8x + 3, what is the measure of each angle?

Solution:

Supplementary angles measure 180˚.

∠Q + ∠R = 180˚

4x + 9 + 8x + 3 = 180˚

12x + 12 = 180˚

12x = 168

x = 14

So,

m∠Q = 4x + 9

m∠Q = 4(14) + 9

 = 56 + 9

m∠Q = 65˚

m∠R = 8x + 3

 = 8(14) + 3

 = 112 + 3

m∠R = 115˚

So, the measure of angles are m∠Q = 65˚ and m∠R = 115˚.