**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.

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