- 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
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°.
- 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.
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 °.
- 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.
- 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.
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°.
- Use a protractor to draw an angle measure for 650.
- How many 600 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 1200 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.