Worksheet adjacent angles will be much useful for the students who would like to practice problems on adjacent angles.

## Adjacent Angles Worksheet - Problems

Problem 1 :

Find the value of  x in the figure shown below. Problem 2 :

Find the value of  x in the figure shown below. Problem 3 :

Find the value of  x in the figure shown below. Problem 4 :

Find the value of  x in the figure shown below. Question 5 :

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. ## Adjacent Angles Worksheet - Solutions

Problem 1 :

Find the value of  x in the figure shown below. Solution :

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

Then,

x + 2x  =  90

3x  =  90

Divide each side by 3.

x  =  30

So, the value of x is 30.

Problem 2 :

Find the value of  x in the figure shown 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.

Then,

(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

So, the value of x is 29.

Problem 3 :

Find the value of  x in the figure shown below. Solution :

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

Then,

(2x + 3) + (x - 6)  =  180

2x + 3 + x - 6  =  180

Simplify.

3x - 3  =  180

3x  =  183

Divide each side by 3.

x  =  61

So, the value of x is 61.

Problem 4 :

Find the value of  x in the figure shown 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.

Then,

(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

So, the value of x is 19.

Question 5 :

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.

Given : The second angle is 4 more than six times of the first angle

Then, the second angle is (6x + 4).

Given : Sum of the two two adjacent angles is 130°.

Then,

x + (6x + 4)  =  130

x + 6x + 4  =  130

Simplify.

7x + 4  =  130

Subtract 4 from each side.

7x  =  126

Divide each side by 7.

x  =  18

Find the value of (6x + 4), whenn x  =  18.

6x + 4  =  6(18) + 4

6x + 4  =  108 + 4

6x + 4  =  112

So, the two angles are 18° and 112°. After having gone through the stuff given above, we hope that the students would have understood how to solve problems on adjacent angles.

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