What is an Angle?
When two lines or rays meet at a point, an angle is formed. The common point is called the vertex of the angle and the two lines or rays are called the sides or arms of the angle.
An angle is denoted by the symbol, ‘∠’.
The angle formed by the rays AB and BC can be written as ‘∠ABC’ or ∠CBA or ∠B
Here B is the vertex of the angle formed.
Types of Angles
We can classify the angles on the basis of their measurement.
- Acute Angle: Angles that measure less than 90°. For example 45°.
- Right Angle: An angle that is equal to 90°.
- Obtuse Angle: Angles that are greater than 90° and less than 180°.
- Straight Angle: An angle that measures 180°.
- Reflex Angle: Angles measuring greater than 180° and less than 360°.
- Complete Angle: An angle that is equal to 360°.
What is a Straight Angle?
An angle with sides in the opposite directions that form a straight line with a measure of 180° is called a straight angle.
Here ∠AOB = 180°
So, ∠AOB is a straight angle.
Straight Angles in our Daily life
In our daily life we come across a number of objects that form a straight angle. Few examples are:
- The angle seen in the see-saw is a straight angle
- The inclined plane of a staircase represents a straight angle
- A flat surface has an angle of 180°
- The hour and minute hands of an analogue clock form a straight angle when the time is 6 o’clock
Properties of Straight Angles
- A straight angle is formed when one side of an angle is opposite in direction to the other side
- Straight angles are exactly half of a revolution
- Straight angles can be formed by joining two right angles
- Straight angles are also called ‘flat angles’
Solved Straight Angle Examples
Example 1: If the hour hand of a clock is at 6 and the minute hand is at 12 what is the measure of the angle formed between them?
Solution:
If the hour hand of a clock is at 6 and the minute hand is at 12, the time is 6 o’clock. Both hands form a straight line, the angle between them is a straight angle, that is, 180°.
Example 2: Find the straight angle pairs from the given figure.
Solution: Two angles combined to form a straight angle are called straight angle pairs.
In this figure:
∠COA + ∠DOA = 180°
∠AOD + ∠BOD = 180°
∠DOB + ∠COB = 180°
∠BOC + ∠AOC = 180°
Therefore, ∠COA and ∠DOA, ∠AOD and ∠BOD, ∠DOB and ∠COB and ∠BOC and ∠AOC form straight angle pairs.
The measure of a straight angle is 180 degree.
Half of a straight angle is 90 degree, which is called a right angle.
We can join two right angles to make a straight angle.
There are four right angles in 360 degree.
There are two straight angles in a complete angle.