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# Angles – Definition, Properties, Example,& Figures ### Key Concepts

• To understand angles and unit angles
• To measure with unit angles
• To measure and draw angles
• To add and subtract angle measures

## Understand Angles and Unit Angles

### Angle:

An angle is the rotation of a ray from an initial point to a terminal point.

## Types of Angles:

There are majorly six types of angles in geometry:

• Acute angle: It lies between 0° to 90°.
• Obtuse angle: It lies between 90° to 180°.
• Right angle: The angle which is exactly equal to 90°.
• Straight angle: The angle which is exactly equal to 180°.
• Reflex angle: The angle which is greater than 180° and less than 360°.
• Full rotation: The complete rotation of an angle equal to 360°.

Unit Angle:

• An angle is measured with units called degrees (ᵒ).
• An angle that turns through 1 / 360 of a circle is called a unit angle.

Examples of angles with their measurements:

### Measure with Unit Angles

Unit angles are measured using a smaller angle to measure a larger angle by repeating the unit.

Unit angle

Example:

What is the measurement of the smaller angle formed by the clock hands when it is 5 o’clock?

## Measure and Draw Angles

### Measuring angles with a protractor

Angles are measured in degrees. The symbol for degrees is a small circle °.

Protractor

• The full circle is 360° (360 degrees).
• A half-circle or a straight angle is 180°.
• A quarter-circle or a right angle is 90°.

## How to measure an angle with a protractor?

A protractor is a tool that is used to measure and draw angles.

Protractor

• Place the midpoint of the protractor on the vertex of the angle.
• Line up one side of the angle with the line zero of the protractor
(Where you see the number 0).
• Read the degrees where the other side crosses the number scale.

Example:

Draw ∠ABC=60° with a ruler and a protractor.

• Draw a straight-line AB
• Place a dot at B.  This dot represents the vertex of the angle.
• Place the center of the protractor at B and the baseline of the protractor along with the arm BA
• Find 60° on the scale and mark a small dot at the edge of the protractor.
• Join the vertex to the small dot with a ruler to form the second arm, BC, of the angle.
• Mark the angle with a small arc as shown.

### Add and Subtract Angle Measures

Finding the measure of an unknown angle by using the known measures.

If ∠ABD = 107°, what is the measure of ∠ABC?

We know that:

∠ABC + ∠CBD = ∠ABD

Plug in the known: n + 37° = 107°

Use the inverse operation to isolate the variable n = 107° – 37° = 70°

So, ∠ABC = 70°.

## Exercise:

1. Use a protractor to draw an angle measure for 650.
2. How many 600 angles does it take to make a full turn?
3. How many degrees are in a twelfth of a full turn?
4. What fraction of the circle does a 1200 angle turn through?
5. What are the measures of an angle?
6. What are the 5 types of angles?
7. What is a zero angle?
8. Find the following missing angles.
1. Find the unknown angles from the figure below.
1. What is the value of x?

### What have we learnt:

• To use and apply vocabulary associated with angles.
• To identify examples of different types of angles.
• To measure and draw angles with a protractor.
• To understand angles and unit angles.
• To add and subtract angle measures.

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