# Types of Angles

## What is Angle?

An angle is formed by two rays with a common endpoint. We measure the size of an angle in DEGREES. **Sides** and **Vertex** are the two components of an angle.

The two rays forming the angle are called **sides**. The common endpoint of the rays is called the **vertex**.

## Types of Angles

There are mainly SIX types of angles based on their measure of the angle. **They include:**

**Acute Angles****Right Angles****Obtuse Angles****Straight Angles****Reflex Angles****Complete Angles**

**Related Topic: Identifying Quadrilaterals**

### 1. Acute Angle

An acute angle is an angle that lies between 0° and 90°. It means an acute angle is greater than 0° but less than 90°. In the above picture, the angle **∠PQR** formed by the intersection of PQ and QR which measures 45°. Thus **∠PQR=45° is an acute angle.** Common examples of acute angles include 15°, 30°, 45°, 80°, etc.

### 2. Right Angle

A right angle is an angle whose measure is exactly 90°. It is mainly formed when two straight lines are perpendicular to each other. **∠MNO = 90°.**

### 3. Obtuse Angle

An obtuse angle is an angle that lies between 90° and 180°. It means an **obtuse angle is greater than 90° but less than 180°**. In the above picture, the angle **∠RST** formed by the intersection of RS and ST which measures 110°. Thus **∠RST=110° is an obtuse angle.** ** **Common examples of obtuse angles include 100°, 115°, 145°, 160°, etc.

### 4. Straight Angle

A straight angle is an angle whose measure is exactly 180°. It is one-half of a whole circle. Straight angle is a combination of acute angle and obtuse angle.

**Acute angle = Straight angle – Obtuse angle**

Example: 180° – 110° = 70° ( acute angle )

**Obtuse angle = Straight angle – Acute angle**

Example: 180° – 40° = 140° ( obtuse angle )

### 5. Reflex Angle

A reflex angle is an angle that lies between 180° and 360º. It means a reflex angle is greater than 180° but less than 360°. [Between straight angle (180º) and a whole turn (360º)]. In the above picture, the angle **∠RST** formed by the intersection of RS and ST which measures 220°. Thus **∠RST=220° is an reflex angle.** Common examples of obtuse angles include: 190°, 215°, 345°, 350°, etc.

### 6. Complete Angle

## Other Types of angles: How to name a pairs of angles

### Complementary Angle

If the sum of two angles is equal to 90°, then they are called complementary angles. One of the complementary angles is said to be the complement of the other.

In the above picture, ∠PQR + ∠RQS = 55° + 35° = 90°.

Example: 53°

To determine the complement, subtract the given angle from 90°.

90° – 53° = 37°,

Therefore, the complement of 53° is 37°.

### Supplementary Angle

If the sum of two angles is equal to 180°, then they are supplementary angles. One of the supplementary angles is said to be the supplement of the other.

In the above picture, ∠ABC + ∠CBD = 60° + 120° = 180°.

Example: 75°

To determine the supplement, subtract the given angle from 180°.

180° – 75° = 105°,

Therefore, the supplement of 75° is 105°.