ADJACENT ANGLES

About "Adjacent angles"

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.  

Adjacent angles - Examples

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

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