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

In the diagram below, the two angles 'a' and 'b' are adjacent. Example 1 :

Find the value of x in the diagram below. Solution :

In the diagram above, x° and (2x)° are adjacent angles and also they are complementary.

x° + (2x)° = 90°

x + 2x = 90

3x = 90

Divide each side by 3.

x = 30°

Example 2 :

Find the value of x in the diagram below. Solution :

In the diagram above, (x + 1)°, (x - 1)° and (x + 3)° are adjacent angles and also they are complementary.

(x + 1)° + (x - 1)° + (x + 3) = 90°

x + 1 + x - 1 + x + 3 = 90

Simplify.

3x + 3 = 90

Subtract 3 from each side.

3x = 87

Divide each side by 3.

x = 29

Example 3 :

Find the value of x in the diagram below. Solution :

In the diagram above, (2x + 3)° and (x - 6)° are adjacent angles and also they are supplementary.

(2x + 3)° + (x - 6)° = 180°

2x + 3 + x - 6 = 180

Simplify.

3x - 3 = 180

3x = 183

Divide each side by 3.

x = 61

Example 4 :

Find the value of x in the diagram below. Solution :

In the diagram above, (5x + 4)°, (x - 2)° and (3x + 7)° are adjacent angles and also they are supplementary.

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

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

Simplify.

9x + 9 = 180

Subtract 9 from each side.

9x = 171

Divide each side by 9.

x = 19

Example 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 each side.

7x  =  126

Divide each side by 7.

x  =  18

6x + 4 = 6(18) + 4

= 112

Hence, the two angles are 18° and 112°. Apart from the stuff given on above, if you need any other stuff in math, please use our google custom search here.

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