**Angle Relationships :**

Two or more angles can be related if certain conditions are met. Here, we will learn different types of angle relationships.

(i) Congruent Angles

(ii) Vertical Angles

(iii) Complementary Angles

(iv) Supplementary Angles

(v) Adjacent Angles

(vi) Adjacent Angles in Parallelogram

(vii) Linear Pair

(viii) Corresponding Angles

(ix) Alternate Interior Angles

(x) Alternate Exterior Angles

(xi) Consecutive Interior Angles

(xii) Consecutive Exterior Angles

Let us see the above different types of angle relationships in detail.

**(i) Congruent angles : **

Congruent angles are angles that have the same measure.

**(ii) Vertical angles : **

Vertical angles have a common vertex, but they are never adjacent angles. And also, vertical angles are always congruent.

**(iii) Complementary angles : **

If the sum of two angles is 90⁰, then those two angles are called as complementary angles.

**(iv) Supplementary angles : **

If the sum of two angles is 180⁰, then those two angles are called as supplementary angles.

**(v) Adjacent angles : **

Adjacent angles are two angles that have a common vertex and a common side.

**(vi) Consecutive angles in Parallelogram: **

Any two consecutive angles of a parallelogram are supplementary.

**(vii) Linear Pair : **

A linear pair is a pair of adjacent angles formed when two lines intersect.

The two angles of a linear pair are always supplementary, which means their measures add up to 180°.

To know about Corresponding Angles, Alternate Interior Angles, Alternate Exterior Angles, Consecutive Interior Angles and Consecutive Exterior Angles in detail,

**Please click here**

**Question 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

Hence, the value of "x" is 8.

**Question 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

Hence, the value of "x" is 8.

**Question 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

Hence the value of "x" is 61.

**Question 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

Hence the value of "x" is 19.

**Question 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

Hence the value of "x" is 31.

**Question 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

Hence the value of "x" is 31.

**Question 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

Hence, the value of "x" is 30.

**Question 8 : **

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 + 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

Hence, the value of "x" is 55.

**Question 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

Hence, the value of "x" is 59.

**Question 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

Hence, the value of "x" is 60.

After having gone through the stuff given above, we hope that the students would have understood "Angle relationships"

Apart from the stuff given above, If you want to know more about "Angle relationships",please click here

Apart from the stuff given on "Angle relationships", if you need any other stuff in math, please use our google custom search here.

After having gone through the stuff given above, we hope that the students would have understood "Relationships between angles".

Apart from the stuff given above, if you want to know more about "Angle relationships", please click here

Apart from the stuff given on "How to measure an angle with protractor", if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM word problems**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**