PROBLEMS ON THE SUM OF ANGLES AROUND A POINT

The sum of the sizes of the angles at a point is 360°.

Find the unknown of the following :

Problem 1 :

Solution :

2x - 10 + 28 + x + x + 30 = 360

4x - 10 + 28 + 30 = 360

4x + 48 = 360

Subtracting 48 on both sides.

4x = 360 - 48

4x = 312

Dividing by 4 on both sides.

x = 312 / 4

x = 78

Problem 2 :

Solution :

b + 311 = 360

Subtracting 311 on both sides.

b = 360 - 311

b = 49

Problem 3 :

Solution :

29 + x = 360

Subtracting 29 on both sides.

x = 360 - 29

x = 331

Problem 4 :

Solution :

m + 92 + 42 = 360

m + 134 = 360

Subtracting 134 on both sides.

m = 360 - 134

m = 226

Problem 5 :

Solution :

60 + 160 + n = 360

220 + n = 360

Subtracting 220 on both sides.

n = 360 - 220

n = 140

Problem 6 :

Solution :

d + 90 + 140 = 360

d + 230 = 360

Subtracting 230 on both sides.

d = 360 - 230

d = 130

Problem 7 :

Solution :

2g + 3g + 90 = 360

5g + 90 = 360

Subtracting 90 on both sides.

5g = 360 - 90

5g = 250

Dividing by 5 on both sides.

g = 250/5

g = 50

Problem 8 :

Solution :

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

7x + 30 + 67 - 31 = 360

7x + 97 - 31 = 360

7x + 66 = 360

Subtracting 66 on both sides.

7x = 360 - 66

7x = 294

Dividing by 7 on both sides.

x = 294/7

x = 42