PROBLEMS ON INTERIOR AND EXTERIOR ANGLES OF A TRIANGLE

Find the values of the variables :

Problem 1 :

Solution :

The sum of the measures of the interior angles of a triangle is 180°.

a° + (a + 25)° + (a - 10)° = 180°

3a° + 15 = 180°

3a° = 180 - 15

3a° = 165

a° = 165/3

a° = 55

Problem 2 :

Solution :

The sum of the measures of the interior angles of a triangle is 180°.

b° + b° + (2b - 40)° = 180°

4b° - 40 = 180

4b° = 180 + 40

4b° = 220

b° = 220/4

b° = 55

Problem 3:

Solution :

Exterior angle = 140 - 2x

Remote interior angles are 80 and x.

Exterior angle = Sum of two remote interior angles

140 - 2x = 80 + x

2x + x = 140 - 80

3x = 60

x = 60/3

x = 20

So, the value of x is 20.

Problem 4 :

Solution :

The sum of the measures of the interior angles of a triangle is 180°.

a° = 55 (corresponding angles)

55° + 48° + b° = 180°

103° + b° = 180°

b° = 180° - 103°

b° = 77

So, the value of a is 55 and b is 77.

Problem 5 :

Solution :

3x - 90 = x

3x - x = 90

2x = 90

x° = 45

The sum of the measures of the interior angles of a triangle is 180°.

45° + 65° + y° = 180°

110° + y° = 180°

y° = 180 - 110

y° = 70

So, the value of x is 45 and y is 70.

Problem 6 :

Solution :

a° = 45 and b° = 85

c° = 45 + 85

c° = 130

c° + d° = 180°

130 + d° = 180°

d° = 180 - 130

d° = 50

So, the values of a, b, c and d are 45, 85, 130 and 50 respectively.