Straight Angle – Definition With Examples

What Is an Angle?

When two straight lines or rays meet at a common endpoint, an angle is formed. The common point of contact of the two rays is called the vertex of an angle. We use the symbol ∠ to represent an angle. We use degrees (°) to measure an angle using a protractor. For example, 45 degrees is represented as 45°. 

Angle definition

There are different types of angles:

  • Acute angle
  • Obtuse angle
  • Right angle
  • Straight angle
  • Reflex angle

What Is a Straight Angle?

In geometry, a straight angle is defined as an angle that is equal to 180 degrees. The reason it is called a straight angle is because it appears as a straight line. In other words, it is an angle whose sides lie in opposite directions from the vertex in the same straight line.  

Straight angle

Straight Angle Examples

Some of its examples in our day-to-day life are:

  • A flat surface has an angle of 180 degrees.
  • A plane inclined staircase.
  • The angle between the minute hand and hour hand at 6:00. 
  • The ruler we use. 
Real life examples of straight angle

Properties of a Straight Angle

Its properties are as follows:

  • It is formed by rotating one ray by 180° with respect to another ray.
  • It reverses the direction of a point
  • It is exactly half of a revolution, i.e., it is half of a complete angle. 
  • It can also be formed by joining two right angles, i.e., 90° + 90° = 180°. 
  • We denoted the straight angle as π
  • It is also known as flat angle. 
Properties of straight angles

Straight Angle Pair

A straight angle pair is a pair of angles that form a straight line. The sum of two or more angles that are in this pair is always equal to 180°. We also call them linear pairs of angles

Linear pair of angles

The image given above shows two angles ∠a = 125° and ∠b = 55°, which together form 180°. The straight angle has a common arm and a common vertex. In the above figure, OS is the common arm and O is the common vertex.

Sometimes there are 3 angles on the straight line. For example, in the figure given below, ∠AOB + ∠BOC + ∠COD = 180°

Three angles forming a straight angle

Solved Examples

Example 1: Find the value of COD in the following diagram.

Three angles forming a straight angle with two angles measuring 60 and 90 degrees

Solution: ∠AOD is a straight angle. 

AOB + ∠BOC + ∠COD = 180°

60° + 90° + ∠COD = 180°

COD = 30°

Example 2: There are _____ 30° in a straight angle.

Solution: A straight angle = 180°

180°30°=6. 

Example 3: Find all the combinations forming straight angles in the following figure.

Two lines VU and WZ intersecting at X with ray XY perpendicular to VU

Solution: Straight angles are:

VXY, ∠YXZ and ∠ZXU

VXY, and ∠YXU

VXZ, and ∠ZXU

VXW and ∠WXU

WXV, ∠VXY and ∠YXZ

WXV, and ∠VXZ

WXY, and ∠YXZWXU and ∠UXZ

Practice Problems

Straight Angle - Definition With Examples

Attend this Quiz & Test your knowledge.

1Which of the following is the measure of 2 right angles?

90°
180°
270°
360°
CorrectIncorrect
Correct answer is: 180°
Two right angles = 2 ✕ 90° = 180°

2Find the value of x if x + 2, x and x + 10 forms a linear pair.

$x = 156°$
$x = 66°$
$x = 56°$
$x = 76°$
CorrectIncorrect
Correct answer is: $x = 56°$
$x + 2 + x + x + 10 = 180°$
$3x + 12 = 180°$
$3x = 168°$
$x = 56°$

3What is not true about the straight angle?

It is made up of two right angles.
It is also known as a flat angle.
In radians, it is called π.
Two straight angles makes a reflex angle.
CorrectIncorrect
Correct answer is: Two straight angles makes a reflex angle.
Reflex angle is an angle lying between a straight angle and a complete angle.

4What fraction of the complete angle is a straight angle?

Half
One - Fourth
One - Eight
One - Fifth
CorrectIncorrect
Correct answer is: Half
Straight angle = 180°
Complete angle = 360°
Fraction = $\frac{180°}{360°}$=$\frac{1}{2}$

Frequently Asked Questions

A straight angle measures 180 degrees and a straight line is a connector of two points.

A pair of supplementary angles is the pair of angles whose sum is 180° but the angles may or may not be adjacent. On the other hand, a straight angle pair is the pair of angles that are always adjacent to each other and have the sum 180°.

The sum of the interior angle and exterior angle is 180° as they lie on the same line.