Angles

Angles

Draw angles

An angle is a measure of an amount of turn. For instance, a complete turn has an angle of 360°

Measuring angles of different size using a protractor

There are several types of angles including:

• acute
• right
• complementary
• obtuse
• supplementary
• reflex angle

Example 1

1. Two angles are supplementary. One angle is three times the other. What are the angles?
2. Two angles are complementary. One angle is 40° greater than the other. What are the angles?

Solution

Drawing angles using a protractor

The angles formed by crossing lines includes vertically opposite angles, alternate angle and corresponding angles.

Vertically opposite angles

The angles on the opposite sides of the crossing lines are equal.

Alternate angles

Consider a line segment crossing two parallel line segments. This line is called a transversal.

The angles within the parallel line segments on the opposite sides of the transversal are equal.

They are also called Z-angles.

Corresponding angles

The angles on the same side of the transversal and on the same side of the parallel lines are equal. They are called corresponding angles and sometimes called F-angles.

There are also three other pairs of corresponding angles in the diagram above. When showing that two angles are equal you must give reason whether they are vertically opposite, or alternate or corresponding angles.