# 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°.

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 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.

## 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.

## 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

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°

# Solved Examples

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

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.

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

1

### Which 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°
2

### Find 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: $x = 56°$
$x + 2 + x + x + 10 = 180°$
$3x + 12 = 180°$
$3x = 168°$
$x = 56°$
3

### What 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.
4

### What 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.