PROBLEMS ON ADJACENT ANGLES

Two angles which have same vertex and share a common arm are called adjacent angles.

∠PAQ and  ∠QAR are adjacent angles.

Adjacent at a point :

The sum of the sizes of the angles at a point is 360 degree

Adjacent angles on a straight line :

The sum of sizes of the angles on a line is 180 degree. The angles are supplementary.

Find the unknown values of the following.

Problem 1 :

Solution :

90 + d + 140 = 360

230 + d = 360

Subtracting 230, we get

d = 360 - 230

d = 130

Problem 2 :

Solution :

2g + 3g + 90 = 360

5g + 90 = 360

5g = 360 - 90

5g = 270

g = 270/5

g = 54

Problem 3 :

Solution :

e + e + e = 360

3e = 360

Dividing by 3, we get

e = 360/3

e = 120

Problem 4 :

Solution :

x + 30 + 2x + 15 = 180

3x + 45 = 180

3x = 180 - 45

3x = 135

x = 135/3

x = 45

Problem 5 :

Solution :

2x + 5 + 15x = 90

17x + 5 = 90

Subtracting 5, we get

17x = 90 - 5

17x = 85

Dividing by 17, we get

x = 85/17

x = 5

Problem 6 :

Solution :

3x + 67 + x - 31 + 3x + 30 = 360

7x + 67 + 30 - 31 = 360

7x + 66 = 360

7x = 360 - 66

7x = 294

x = 294/7

x = 42