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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