## 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 ∠*YXZ*∠*WXU* and ∠*UXZ*

## Practice Problems

## Straight Angle - Definition With Examples

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

Two right angles = 2 ✕ 90° = 180°

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

$x + 2 + x + x + 10 = 180°$

$3x + 12 = 180°$

$3x = 168°$

$x = 56°$

### 3What is not true about the straight 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?

Straight angle = 180°

Complete angle = 360°

Fraction = $\frac{180°}{360°}$=$\frac{1}{2}$

## Frequently Asked Questions

**What is the difference between a straight angle and a straight line?**

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

**What is the difference between a pair of supplementary angles and straight angle pairs?**

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°.

**What is the sum of the interior angle and exterior angle?**

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