TYPES OF ANGLES AND RELATIONSHIPS 

What is angle ?

A line is an infinite number of points between two end points. Where two lines meet or cross, they form an angle.

An angle is an amount of rotation. It is measured in degrees.

Different types of angles involving straight lines :

• Complementary angles Angles that add up to 90°
• Supplementary angles Angles that add up to 180°

Adjacent angles :

Angle that have common vertex and a common arm.

Adjacent angles on a straight line add upto 180 degree.

Perpendicular lines :

Lines that meet or cross at 90°

Here AB ⊥ CD.

Vertically opposite angles :

When two straight lines intersect the angles opposite each other are called vertically opposite angles.

Vertically opposite angles are equal to each other.

Parallel Lines and Transversal

Transversals creates three important types of angles, namely:

1. Corresponding angles

2. Co-interior angles

3. Alternating angles

Corresponding angles are in the same position as each other.

Co-interior angles are between the lines and on the same side of the transversal. They are “inside together”.

Alternate angles are between the lines and on alternate (opposite) sides of the transversal.

Calculate the size of the variables.

Problem 1 :

Solution:

In the diagram above, a and 50° are supplementary angles.

a + 50° = 180°

a = 180 - 50

a = 130

Problem 2 :

Solution:

In the diagram above, 10°, 60° and b are supplementary angles.

10° + 60° + b = 180°

70° + b = 180°

b = 180 - 70

b = 110

Problem 3 :

Solution:

In the diagram above, 2c and 120° are supplementary angles.

2c +120° = 180°

2c = 180 - 120

2c = 60

c = 30

Problem 4 :

Solution:

In the diagram above, (d + 20°) and d are supplementary angles.

d + 20° + d = 180°

2d + 20 = 180

2d = 180 - 20

2d = 160

d = 80°

Problem 5 :

Solution:

l || k

x + 51° = 180°

x = 180 - 51

x = 129°

y = 100°

y + z = 180°

z = 180 - 100

z = 80°

So, x = 129°, y = 100° and z = 80°

Problem 6 :

Solution:

∠NOP = ∠MNO (alternate interior angle)

x = 62°

Problem 7 :

Solution:

In the figure, let b = 71°

Because line UV is parallel to line WX.

So we can get,

x = b = 71°

The two lines are parallel and the interior alternate angles are equal. b and x is interior alternate angles.

a = 180° - x

a = 180 - 71

a = 109°

Because line RQ is parallel to line TS.

y = a = 109°

Two lines are parallel and corresponding angles are equal. a and y is corresponding angles.

So, x = 71° and y = 109°.