A day full of math games & activities. Find one near you.

Straight Angle

A straight angle measures 180° and looks like a straight line, therefore, it is a mathematical way of expressing a straight line. It is an angle whose arms lie in opposite directions from the vertex and they join together to form 180°. Let us learn more about the straight angle in this article.

1.	Straight Angle Definition
2.	Properties of a Straight Angle
3.	Straight Angle Degree
4.	Drawing a Straight Angle Using a Protractor
5.	FAQs on Straight Angles

Straight Angle Definition

Whenever two rays join together they form an angle and the angle subtended by two rays in opposite directions is called a straight angle. In geometry, a straight angle is an angle whose vertex point has a value of 180 degrees.

Straight angle

In other words, when the arms of the angle lie in the opposite direction, they form a straight angle. The arms make a straight line through the vertex.

Properties of a Straight Angle

The important properties of straight angles are as follows.

A straight angle is formed by rotating one ray by 180° with respect to another ray.
A straight angle reverses the direction of a point.
A straight angle is exactly half of a revolution.
A straight angle can also be formed by joining two right angles.

Straight Angle Degree

The degree or the measure of a straight angle is always 180º. In the conventional angle measuring system, we consider the right angle as 90º and the angle around a point to be 360º. The straight angle is made up of two right angles. Observe the figure given below to understand this fact.
Straight angle degree

Drawing a Straight Angle Using a Protractor

A straight angle can be constructed easily using a protractor. Follow the steps given below to draw a straight angle using a protractor:

Step 1: Draw a straight line and name it as AB and mark an arrowhead on B.
Step 2: Place the protractor on line AB such that the baseline of the protractor is over the line AB. Ensure that B is pointing to 0°.
Step 3: Starting from 0° in the inner scale and keeping the protractor fixed on its place, move your pencil slowly until you reach 180°. Mark this point as C and also mark an arrowhead here.
Step 4: Join point C with line AB. Thus, a straight angle CAB of 180º is formed.

The following figure shows how a straight angle is constructed using these steps.

Construction of a Straight Angle Using Protractor

Straight Angle Pair

A pair of angles that form a straight line is called a straight angle pair. The sum of two angles that are in a straight angle pair is always equal to 180°. They are also known as linear pairs of angles. The image shown below shows two angles a = 135° and b = 45°, which together form 180°. The straight angle pairs have the following properties in common. They have a common arm and a common vertex. In the following figure, QS is the common arm and Q is the common vertex.

Straight angle pair

Straight Angles in Real Life

We come across straight angles often in our day-to-day life. Some examples of a straight angle are given below.

The clock showing 6 o'clock forms a straight angle.
A rectangular tabletop represents a straight angle.
Your line of sight is the perfect example of a straight angle.

All the angles given below are straight angles. They differ only in orientation. Following these, we can find many straight angles around us.

Various Straight Angles

Topics Related to Straight Angles

Important Notes:

A straight angle is formed by rotating one ray by 180° with respect to another ray.
A straight angle is exactly half of a revolution.
In radians, the straight angle is denoted by π.
A straight angle reverses the direction of a point.
A straight angle is also called a ‘flat angle’.
A straight angle pair is a set of two adjacent angles on a straight line that add up to 180°
If ∠A + ∠B = 180°, then ∠A and ∠B form a straight angle pair (linear pair).

Straight Angle Examples

Example 1: Identify the straight angle pairs in the following figure.

Solution:

Here, ∠AOC,∠BOD are straight angles. ∠AOD and ∠COD have a common arm OD and a common vertex 'O'. They are on the same straight line AC. So,∠AOD and ∠COD form a straight angle pair. It can be seen that:

∠1 + ∠2 = 180°
∠2 + ∠3 = 180°
∠3 + ∠4 = 180°
∠4 + ∠1 = 180°
So, there are 4 straight angle pairs in all.
Example 2: If the hour hand of a clock is at 6 and the minute hand is at 12, what is the angle thus formed? Does it form a straight angle or a right angle?

Solution:

If the hour hand of a clock is at 6 and the minute hand is at 12, the time is 6 o'clock and the hands form a straight line. Since the angle between the hands at 6'o clock is 180º, the clock shows a straight angle.
Example 3: Tia states that, "If two congruent angles form a linear pair or a straight angle pair, the angles are right angles." Check whether she is correct or not.
Solution:

If two angles form a straight angle pair (linear pair) then they both add up to 180º, which means ∠A + ∠B = 180º

Here the angles are congruent,

∠A = ∠B
∠A + ∠B = 180°
2∠A = 180
∠A = 90°
∠A = ∠ B = 90°
Therefore, Tia is correct.

go to slide go to slide go to slide

How can your child master math concepts?

Math mastery comes with practice and understanding the ‘Why’ behind the ‘What.’ Experience the Cuemath difference.

Book a Free trial Class

Practice Questions on Straight Angle

go to slide go to slide

FAQs on Straight Angles

What is a Straight Angle in Math?

When two rays or arms of an angle are in opposite directions, they make a straight line. The angle formed by these two rays is 180°. This is called a straight angle.

What is the Measure of a Straight Angle?

A straight angle measures 180° because it is formed when two rays are joined in opposite directions.

What is Half the Measure of a Straight Angle?

90° is half the measure of a straight angle. It is also called a right angle.

Can we say that a Straight Line is a Straight Angle?

Yes, a straight line with two endpoints makes an angle of 180°. So we can consider a straight line as a straight angle.

What Fraction of a Straight Angle is a Right Angle?

A right angle measures 90° and a straight angle measures 180°. Therefore, a right angle is half of a straight angle. 1/2 × 180° = 90°.

What is Greater than a Right Angle and Less than a Straight Angle?

An angle which is greater than a right angle (90°) and less than a straight angle (180°) is called an obtuse angle.

How many Right Angles are there in a Straight Angle?

Since a right angle measures 90° and a straight angle measures 180°, this means that there are two right angles in a straight angle. 90° + 90° = 180°

What does a Straight Angle Look Like?

A straight angle looks like a straight line whose angle is 180°. The best example of a straight angle is when the hour hand of a clock is at 6 and the minute hand is at 12, the time is 6 o'clock and the hands form a straight line or a straight angle.

Math worksheets and
visual curriculum