**Adjacent angles :**

Two angles are adjacent if they have a common vertex and a common side.

In the diagram given below, the two angles "a" and "b" are adjacent.

**Question 1 : **

Find the value of "x" in the figure given below.

**Solution :**

From the picture above, it is very clear that the angles "x" and "2x" are adjacent and also they are complementary angles.

So, we have x + 2x = 90°

3x = 90°

x = 30°

Hence the value of "x" is 30°.

**Question 2 : **

Find the value of "x" in the figure given below.

**Solution :**

From the picture above, it is very clear that the angles (x+1), (x-1) and (x+3) are adjacent and also they are complementary angles.

So, we have (x+1) + (x-1) + (x+3) = 90

3x + 3 = 90

3x = 87

x = 29

Hence the value of "x" is 29.

**Question 3 : **

Find the value of "x" in the figure given below.

**Solution :**

From the picture above, it is very clear that (2x+3) and (x-6) are adjacent and also they 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 figure given below.

**Solution :**

From the picture above, it is very clear (5x+4), (x-2) and (3x+7) are adjacent and also they 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 : **

The sum of the two two adjacent angles is 130°. If the second angle is 4 more than six times of the first angle, find the two angles.

**Solution : **

Let "x" be the first angle.

Then, the second angle is 6x + 4

Sum of the two angles = 130°

x + 6x + 4 = 130

7x + 4 = 130

Subtract 4 from both sides

(7x + 4) - 4 = 130 - 4

7x = 126

Divide both sides by 7

(7x) / 7 = (126) / 7

x = 18

Then,

6x + 4 = 6(18) + 4

6x + 4 = 108 + 4

6x + 4 = 112

Hence, the two angles are 18° and 112°.

After having gone through the stuff given above, we hope that the students would have understood about the angles which are adjacent.

Apart from the stuff given above, if you want to know more about the angles which are adjacent, 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**