## What is an Angle Measure?

**An angle is formed when two lines or rays meet at a common point. The common point is known as the vertex. **

In geometry, an angle measure can be defined as the measure of the angle formed by the two rays or arms at a common vertex.

For example, in the illustration below, the yellow region measures the span of the angle.

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## How to Find the Measure of an Angle?

Angles are measured in degrees (°) using a protractor. A protractor is a measuring device that is used to calculate or draw angles in terms of degrees.

For example, in the image below, we see that using a protractor, the black arrow points to 100°, crossing 90°. Hence, the measure of the angle is 100°.

To determine the angle measure with a protractor, follow the steps below:

- Position the middle point or midpoint of the protractor on the vertex of the angle.
- Place one side of the angle on the zero-marked line of the protractor (at the point you observe the numeral 0).
- Find the degree measure at which the other side of the protractor points the angle.

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## Types of Angles

There are many kinds of angles in geometry: acute, obtuse, reflex, straight, and right angle. Each angle has a different measure.

There are also special types of angle pairs. Let’s first take a look at the various types of angles.

**Types of Angles Based on Measurement**

**Right Angle**

An angle between two rays measuring exactly 90° is called a right angle.

**Acute Angle**

An acute angle is formed when two rays intersect at the vertex and form an angle smaller than 90°. Some examples of acute angles are 20°, 40°, 60°, and 80°.

**Obtuse Angle**

Obtuse angles are any angles that measure greater than 90° and smaller than 180°. Some examples of obtuse angles include 110°, 130°, 145°, and 165°.

**Straight Angle**

Straight angles are, as the name implies, straight lines. The two rays that form a straight angle are opposite each other. The angle between the two rays is 180°. Two adjacent right angles can be combined to create a straight angle.

**Reflex Angle**

A reflex angle is an angle greater than 180° or less than 360°. Some examples of reflex angles include

210° and 250°.

### Types of Angles Based on Rotation

**Positive Angles**

An angle with the degree of the ray’s rotation from its starting point to its final position in a counterclockwise direction is referred to as a positive angle. The direction counterclockwise is considered to be a positive direction within the sense of angle.

**Negative Angles**

Negative angles are angles that are rotated in the clockwise direction from the base.

**Types of Angle Pairs**

A pair of angles is a combination of two angles. Let’s learn more about the different angle pairs in geometry.

**Adjacent Angles**

The following conditions must be met for two angles to be considered adjacent:

- The two angles share the same vertex.
- The two angles share one arm.

**Complementary Angles**

Complementary angles are angles whose sum equals 90°. Complementary angles can be adjacent or non-adjacent.

For example, the given image shows adjacent and non-adjacent complementary angles.

In the first image, the sum of angle measures is $30°+ 60°=90°$

In the second image, the sum of angle measures is $50°+ 40°=90°$

#### Supplementary Angles

Supplementary angles are angles which add up to 180° i.e. the sum of their angle measures is 180°.

If the two supplementary angles are adjacent to each other, they are called ‘angles in linear pair’.

For example, in the above image, the angles measuring 140° and 40° are supplementary and adjacent. So, they form a linear pair.

On the other hand, the angles measuring 150° and 30° are supplementary but not adjacent.

**Corresponding Angles**

Consider two parallel lines. When these are intersected by another line, i.e, a transversal, the angles created in the corresponding corners are known as corresponding angles.

**Vertical Angles**

When two lines intersect, the angles opposite each other are equal. These are called vertical angles or vertically opposite angles.

## Let’s sing!

Acute angles are a tiny bit smaller than normal.

The corner of a wall is at a right angle

The obtuse angle at 2.50 in the daytime

Straight bend in a straw made of soda-lime

There are so many angles, even in mimes!

## Solved Examples

**1. If ∠A is 55°, then what type of angle is it?**

**Solution**: $∠A = 55°$

An acute angle is formed when two rays intersect at the vertex and form an angle that is smaller than 90°. Since a 55° angle is smaller than 90°, it is an acute angle.

**2. What is an angle pair measuring 55° and 35° called?**

**Solution**: Complementary angles are angles whose sum equals 90°.

Since the sum of these angles equals $90**°** (55° + 35° = 90°)$, we call them complementary angles.

**3. If ∠P is 210°, then what type of angle is it?**

**Solution**: A reflex angle is an angle greater than 180° or less than 360°. Since **∠**P measures 210**°,** it is a reflex angle.

## Practice Problems

## Angle Measure

### What is a 90° angle called?

In geometry and trigonometry, a right angle is an angle of precisely 90°.

### What are angles measuring 80° and 10° called?

Two angles are called complementary if their measures add to 90°.

### What is a 45° angle called?

An angle measuring less than 90° is called an acute angle.

### What are angles measuring 120° and 60° called?

Two angles are called supplementary when their measures add up to 180°.

## Frequently Asked Questions

**What are the two conditions to be met for an angle to be called an adjacent angle?**

The following conditions must be met for two angles to be considered adjacent:

- The two angles share the same vertex.
- The two angles share one arm.

**What kinds of angles can be measured using a protractor?**

A protractor can be used to measure the following kinds of angles: acute angles, straight angles, obtuse angles, right angles, full rotation angles, and reflex angles.

**Which sign is used to represent an angle?**

The sign ∠ is used to represent an angle.