# COMPLEMENTARY AND SUPPLEMENTARY ANGLES WORD PROBLEMS

Complementary angles :

Two angles are complementary, if the sum of their measures is equal to 90.

Supplementary angles :

Two angles are supplementary angles if the sum of their measures is equal to 180 degrees.

Problem 1 :

An angle measures 38° less than its complement.

Solution :

The required angle be x.

If two angles are complementary to each other, then its sum will be 90 degree.

Required angle = 90 - 38

= 52

So, the required angle is 52 degree.

Problem 2 :

Find the measure of angle that is 10° more than its complement.

Solution :

The required angle be x.

If two angles are complementary to each other, then its sum will be 90 degree.

Required angle - Its complement = 10

x - (90 - x) = 10

x - 90 + x = 10

2x = 10 + 90

2x = 100

x = 50

= 52

So, the required angle is 52 degree.

Problem 3 :

Find the measure of an angle that is 30° less than its supplement.

Solution :

Let x be the required angle.

Its supplement will be 180 - x

(180 - x) - 30 = x

180 - x - 30 = x

150 - x = x

150 = x + x

2x = 150

x = 150/2

x = 75

So, the required angle is 75 degree.

Problem 4 :

The supplement of an angle is thirty more than twice the angle.

Solution :

Let x be the required angle.

Its supplement = 180 - x

180 - x = 2x + 30

180 - x - 2x = 30

180 - 3x = 30

180 - 30 = 3x

3x = 150

x = 150/3

x = 50

So, the required angles is 50.

Problem 5 :

An angle is one-third its supplement.

Solution :

Let x be the required angle

ITs supplement will be 180 - x

x = (1/3) of (180 - x)

x = (180 - x)/3

3x = 180 - x

3x + x = 180

4x = 180

x = 180 / 4

x = 45

Problem 6 :

Find the measure of an angle whose complement and supplement sum is 194 degrees.

Solution :

If x be the angle measure, its complement will be 90 - x and its supplement will be 180 - x

90 - x + 180 - x = 194

270 - 2x = 194

-2x = 194 - 270

-2x = -76

x = 76/2

x = 38

Problem 7 :

One of two supplementary angles is 35 degrees more than twice the other.

Solution :

Let x and 180 - x be the supplementary angles.

180 - x = 2x + 35

180 - 35 = 2x + x

145 = 3x

x = 145/3

x = 48.3

Problem 8 :

An angle is 30 less than half its complement.

Solution :

Let x be the angle and its complement will be 90 - x

x = (90 - x)/2 - 30

x = (90 - x - 60)/2

2x = 30 - x

2x + x = 30

3x = 30

x = 30/3

x = 10

So, the required angle is 10.

Problem 9 :

The supplement of an angle is twenty four degree less than five times the angle. Find the measure of each angle.

Solution :

Let x and 180 - x will be supplementary angle.

180 - x = 5x - 24

180 - x - 5x = -24

180 - 6x = -24

180 + 24 = 6x

6x = 204

x = 204/6

x = 34

Problem 10 :

Two complementary angles have measures in the ratio 1 : 5. Find the measure of the larger angle.

Solution :

Let x and 90 - x will be the complementary angles.

From the given ratio, x and 5x are the required angles.

x + 5x = 90

6x = 90

x = 90/6

x = 15

Applying the value of x, we get

x = 15, 5x = 5(15) ==> 75

So, the required larger angle measure is 75 degree.

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