PROBLEMS ON COINTERIOR ANGLES

When two parallel lines are cut by a third line, co-interior angles are supplementary.

Co-interior are also called as consecutive interior angles.

Find the values of the variables in the following :

Problem 1 :

Solution :

y and 127 are cointerior angles are consecutive interior angles.

y + 127 = 180

Subtracting 127 on both sides.

y = 180 - 127

y = 53

Problem 2 :

Solution :

z and 70 are cointerior angles are consecutive interior angles.

z + 70 = 180

Subtracting 70 on both sides.

y = 180 - 70

y = 110

Problem 3 :

Solution :

g and 57 are cointerior angles are consecutive interior angles.

g + 57 = 180

Subtracting 57 on both sides.

g = 180 - 57

g = 123

Problem 4 :

Solution :

Since the opposite sides are parallel.

Problem 5 :

Solution :

19x - 2 + 42x - 1 = 180

61x - 3 = 180

Adding 3.

61x = 180 + 3

61x = 183

Dividing by 61 on both sides.

x = 183/61

x = 3

Problem 6 :

Solution :

4 + 16x + 80 = 180

16x + 84 = 180

Subtracting 84.

16x = 180 - 84

16x = 96

Dividing by 16 on both sides.

x = 96/16

x = 6

Problem 7 :

Solution :

97 + 15x + 8 = 180

15x + 105 = 180

Subtracting 105 on both sides.

15x = 180 - 105

15x = 75

Dividing by 15 on both sides.

x = 75/15

x = 5