### 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
*B*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:**

- Use a protractor to draw an angle measure for 65
^{0}. - How many 60
^{0}angles does it take to make a full turn? **How many degrees are in a twelfth of a full turn?**- What fraction of the circle does a 120
^{0}angle turn through? - What are the measures of an angle?
- What are the 5 types of angles?
- What is a zero angle?
- Find the following missing angles.

- Find the unknown angles from the figure below.

- 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.