Basic Geometry - Angles

Definition

Angle is a geometric figure formed by two lines or rays which meet at a point.

Look at the following figure.

The angle beside can be named as follow:

• Angle B, writen as .
• Angle ABC, writen as or angle CBA, writen as , or
• Angle x (by a small letter)

Angle Measuring

One full turn/ One full rotation   = 360º
Half turn = 1/2 one full rotation  = 1/2 . 360º = 180º 

Quarter turn = 1/4 one full rotation = 1/4 . 360º = 90º

Types of angle

1. Angle measure less than 90º is called acute angle.

2. Angle measure 90º is called right angle.

3. Angle measure larger than 90º but less than 180º is called obtuse angle.

4. Angle measure 180º is called straight angle or two right angles.

5. Angle measure more than 180º and less than 360º is called reflex angle.

Example 1

Rewrite each angle in degree
a. 1/3 of a full turn = ... °     
b. 1/4 of a right angle = ... °

c. 1.25 of a straight angle = ... °

Solution:

a. one full turn = 360°

   1/3 of a full turn = 1/3 . 360° = 120°

b. one right angle = 90°

   1/4 of right angle = 1/4 . 90° = 22,5°

c. one straight angle = 180°

   1,25 of straight angle = 1,25 . 180° = 225°

Example 2

a. 60° = ...of a right angle = ...of a straight angle = ...of one full turn.

b. 135° =  ...of a right angle = ...of a straight angle = ...of one full turn.

Solution:

a. The main objective of the problem is to determine the simplest fraction. Look at the following process:

one right angle = 90°

so the ratio is: 60°/90° = 2/3 then 60° = 2/3 of right angle.

one straight line = 180°

so the ratio: 60°/180° =  1/3 then 60° = 1/3 of straight angle.

one full turn = 360°

so the ratio = 60°/360° = 1/6 then 60° = 1/6 of one full turn.

60° = 2/3 of a right angle = 1/3 of a straight angle = 1/6 of one full turn.

b. Using the same method,

135° = 3/2 of a right angle = 3/4 of a straight angle = 3/8 of one full turn.

Example 3
Determine the type of angle from 4/3 of a right angle.
solution:
one right angle = 90°
4/3 of one right angle = 4/3 . 90° = 120°
120° is between 90° and 180° then the type of 120° is an obtuse angle.

-Vn-