WORD PROBLEMS ON COMPLEMENTARY AND SUPPLEMENTARY ANGLES

Problem 1 :

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

Solution :

Since angles A and B are complementary,

m∠A + m∠B = 90

3x - 8 + 5x + 10 = 90

8x + 2 = 90

Subtracting 2 on both sides.

8x = 90 - 2

8x = 88

Dividing by 8 on both sides.

x = 88/8

x = 11

So, the required angles measures are 25° and 65°.

Problem 2 :

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

Solution :

Since angles Q and R are supplementary, they add up to 180 degree.

m∠Q + m∠R = 180

4x + 9 + 8x + 3 = 180

12x + 12 = 180

Subtracting 12 on both sides.

12x = 180 - 12

12x = 168

Dividing by 12 on both sides, we get

x = 168/12

x = 14

So, the angle measures are 65 and 115.

Problem 3 :

Find the measure of two complementary angles ∠A and ∠B, if m∠A = 7x + 4 and m∠B = 4x+ 9.

Solution :

Since ∠A and ∠B are complementary, they add upto 90.

m∠A + m∠B = 90

7x + 4 + 4x + 9 = 90

11x + 4 + 9 = 90

11x + 13 = 90

Subtracting 13 on both sides.

11x = 90 - 13

11x = 77

x = 77/11

x = 7

So, the required angles are 53 and 37.

Problem 4 :

The measure of an angle is 44 more than the measure of its supplement. Find the measures of the angles.

Solution :

Let x be the required angle, its supplement be 180-x.

x = 180-x + 44

x = 224 - x

Add x on both sides.

x + x = 224

2x = 224

Divide by 2.

x = 224/2

x = 112

180 - x ==> 180 - 112 ==> 68

So, the required angles are 112 and 68.

Problem 5 :

What are the measures of two complementary angles if the difference in the measures of the two angles is 12.

Solution :

Let x be a angle, its complementary angle is 90 - x.

x - (90 - x) = 12

x - 90 + x = 12

2x = 12 + 90

2x = 102

Dividing by 2 on both sides.

x = 102/2

x = 51

90 - 51 ==> 39

So, the required angles are 39 and 51.

Problem 6 :

Find the measures of two supplementary angles ∠N and ∠M if the measure of angle N is 5 less than 4 times the measure of angle M.

Solution :

∠N = 4∠M - 5

∠N and ∠M are supplementary.

∠N + ∠M = 180

4∠M - 5 + ∠M = 180

5∠M = 180 + 5

5∠M = 185

Dividing by 5

∠M = 185/5

∠M = 37

Applying the value of ∠M, to find ∠N.

∠N = 4(37) - 5

∠N = 148 - 5

∠N = 143

Problem 7 :

Suppose ∠T and ∠U are complementary angles. Find x, if ∠T = 16x - 9 and ∠U = 4x - 1.

Solution :

Since ∠T and ∠U are complementary angles.

∠T + ∠U = 90

16x - 9 + 4x - 1 = 90

20x - 10 = 90

Add 10 on both sides.

20x = 90 + 10

20x = 100

x = 100/20

x = 5

So, the required angles are 71 and 19.

Problem 8 :

Two angles are vertical in relation. One angle is 2y and the other angle is y + 130. Find each angle measure.

Solution :

If two angles are vertical, then they will have the same measure.

2y = y + 130

2y - y = 130

y = 130

2y = 260 and y + 130 = 260

So, those two angels are 260 and 260.

Problem 9 :

The measure of two supplementary angles are in the ratio 4 : 2, Find those two angles.

Solution :

Let the required angles be 4x and 2x.

4x + 2x = 180

6x = 180

Divide by 6, we get

x = 180/6

x = 30

4x = 4(30) ==> 120

2x = 2(30) ==> 60

So, the required those two angles are 60 and 120.