**Angle Relationships Worksheet :**

Worksheet given in this section will be much useful for the students who would like to practice problems on angle relationships.

Before look at the worksheet, if you would like to know about the different types of angle relationships,

**Problem 1 : **

Find the value of x in the diagram given below.

**Problem 2 : **

Find the value of x in the diagram given below.

**Problem 3 : **

Find the value of x in the diagram given below.

**Problem 4 : **

Find the value of x in the diagram given below.

**Problem 5 : **

Find the value of x in the diagram given below.

**Problem 6 : **

Find the value of x in the diagram given below.

**Problem 7 : **

In the diagram given below, l_{1 }lines l_{2} are parallel and t is a transversal. Find the value of x.

**Problem 8 : **

In the diagram given below, l_{1 }lines l_{2} are parallel and t is a transversal. Find the value of x.

**Problem 9 : **

In the diagram given below, a_{ }lines b are parallel and t is a transversal. Find the value of x.

**Problem 10 : **

In the diagram given below, find the value of x.

**Problem 1 : **

Find the value of x in the diagram given below.

**Solution :**

In the diagram above, it is very clear that the angle measures (6x + 4)° and (4x + 6)° are complementary.

So, we have

(6x + 4)° + (4x + 6)° = 90°

6x + 4 + 4x + 6 = 90

10x + 10 = 90

Subtract 10 from both sides.

10x = 80

Divide both sides by 10.

x = 8

So, the value of x is 8.

**Problem 2 : **

Find the value of x in the diagram given below.

**Solution :**

In the diagram above, it is clear that the angle measures (4x + 7)° and (6x + 3)° are complementary.

So, we have

(4x + 7)° + (6x + 3)° = 90°

4x + 7 + 6x + 3 = 90

10x + 10 = 90

Subtract 10 from both sides.

10x = 80

Divide both sides by 10.

x = 8

So, the value of x is 8.

**Problem 3 : **

Find the value of x in the diagram given below.

**Solution :**

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

So, we have

(2x + 3)° + (x - 6)° = 180°

2x + 3 + x - 6 = 180

3x - 3 = 180

3x = 183

x = 61

So, the value of x is 61.

**Problem 4 : **

Find the value of x in the diagram given below.

**Solution :**

In the diagram above, it is clear that (5x+4)°, (x-2)° and (3x+7)° are supplementary angles.

So, we have

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

5x + 4 + x -2 + 3x + 7 = 180

9x + 9 = 180

9x = 171

x = 19

So, the value of x is 19.

**Problem 5 : **

Find the value of x in the diagram given below.

**Solution :**

In the diagram above, it is clear that (3x+7)° and 100° are vertical angles.

Because (3x+7)° and 100° are vertical angles, they are congruent.

So, we have

(3x + 7)° = 100°

3x + 7 = 100

Subtract 7 from both sides.

3x = 93

Divide both sides by 3.

x = 31

So, the value of x is 31.

**Problem 6 : **

Find the value of x in the diagram given below.

**Solution :**

In the diagram above, it is clear that (x + 33)° and 98° form a linear pair.

Because the two angles of a linear pair are always supplementary, we have

(x + 33)° + 98° = 180°

x + 33 + 98 = 180

x + 131 = 180

Subtract 131 from both sides.

x = 49

So, the value of x is 31.

**Problem 7 : **

In the diagram given below, l_{1 }lines l_{2} are parallel and t is a transversal. Find the value of x.

In the above diagram, (2x + 20)° and (3x - 10)° are corresponding angles.

When two parallel lines are cut by a transversal, corresponding angles are congruent.

So, we have

(2x + 20)° = (3x - 10)°

2x + 20 = 3x - 10

30 = x

So, the value of x is 30.

**Problem 8 : **

_{1 }lines l_{2} are parallel and t is a transversal. Find the value of x.

In the above diagram, (2x + 10)° and (x + 5)° are consecutive interior angles.

When two parallel lines are cut by a transversal, consecutive interior angles are supplementary.

So, we have

(2x + 10)° + (x + 5)° = 180°

2x + 10 + x + 5 = 180

3x + 15 = 180

Subtract 15 from both sides.

3x = 165

Divide both sides by 3.

x = 55

So, the value of x is 55.

**Problem 9 : **

In the diagram given below, a_{ }lines b are parallel and t is a transversal. Find the value of x.

In the diagram diagram, (2x + 26)° and (3x - 33)° are alternate interior angles.

When two parallel lines are cut by a transversal, alternate interior angles are congruent.

So, we have

(2x + 26)° = (3x - 33)°

2x + 26 = 3x - 33

59 = x

So, the value of x is 59.

**Problem 10 : **

In the diagram given below, find the value of x.

**Solution : **

In the diagram diagram, it is clear that AB||CD and AD||BC.

So ABCD is a parallelogram.

In a parallelogram, two consecutive angles are always supplementary.

Then, we have

x° + (2x)° = 180°

x + 2x = 180

3x = 180

Divide both sides by 3.

x = 60

So, the value of x is 60.

After having gone through the stuff given above, we hope that the students would have understood how to solve problems using relationship between angles.

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