Identification & Properties of Angles – JSS1 Mathematics Lesson Note (Third Term)

An angle is the amount of turn between two lines that meet at a point, and it is measured in degrees (°).

Behavioural objectives

By the end of the lesson, students should be able to:

1. identify straight, right, obtuse, acute and reflex angles by their measures;
2. state the meaning of adjacent, complementary and supplementary angles;
3. state the properties of vertically opposite angles and corresponding angles;
4. identify obtuse-angled and acute-angled triangles.

What is an angle?

An angle is formed when two straight lines (arms) meet at a common point called the vertex.

• Vertex: the point where the two arms meet, often labelled O.
• Arms: the two straight lines that form the angle.
• Degree (°): the unit used to measure the size of an angle.
• Protractor: the instrument used to measure and draw angles.
• Naming: an angle can be written as angle A, or <A for short.
• Theta (ϴ): a Greek letter used to stand for the size of an angle.

What are the types of angles by size?

There are five types of angles by size: acute, right, obtuse, straight and reflex.

What is a straight angle?

A straight angle is an angle that measures exactly 180°.

• Shape: it looks like a straight line.
• Size: ϴ = 180°.

What is a right angle?

A right angle is an angle that measures exactly 90°.

• Size: ϴ = 90°.
• Example: the corner of a page, a classroom door or a chalkboard.

What is an obtuse angle?

An obtuse angle is an angle greater than 90° but less than 180°.

• Size: 90° < ϴ < 180°.
• Example: 120° and 150° are obtuse angles.

What is an acute angle?

An acute angle is an angle greater than 0° but less than 90°.

• Size: 0° < ϴ < 90°.
• Example: 30° and 65° are acute angles.

What is a reflex angle?

A reflex angle is an angle greater than 180° but less than 360°.

• Size: 180° < ϴ < 360°.
• Example: 200° and 300° are reflex angles.

What are the pairs of angles and their properties?

Angles are named by how they relate to each other: adjacent, complementary, supplementary, vertically opposite and corresponding angles.

What are adjacent angles?

Adjacent angles are two angles that share the same vertex and have a common side (line).

• Common vertex: both angles start from the same point, usually labelled O.
• Common side: one arm belongs to both angles.

What are complementary angles?

Complementary angles are two angles whose sum is 90°.

• Rule: <A + <B = 90°.
• Example: 30° and 60° are complementary.
• Note: <A and <B mean ‘angle A’ and ‘angle B’ respectively.

What are supplementary angles?

Supplementary angles are two angles whose sum is 180°.

• Rule: <A + <B = 180°.
• Example: 110° and 70° are supplementary.
• On a straight line: angles that sit side by side on a straight line add up to 180°.

What are vertically opposite angles?

Vertically opposite angles are the angles that face each other when two straight lines intersect.

• Property: vertically opposite angles are equal in magnitude.
• Pairs: two straight lines that cross make two pairs of vertically opposite angles.

What are corresponding angles?

Corresponding angles are angles in matching positions when a transversal crosses two parallel lines.

• Transversal: the line that crosses the two parallel lines.
• Property: corresponding angles are equal in magnitude.
• Position: each angle is in the same place at its own crossing point, for example both above the line and to the right of the transversal.

What are obtuse-angled and acute-angled triangles?

A triangle can be named by the size of its angles, and the three angles of any triangle add up to 180°.

What is an obtuse-angled triangle?

An obtuse-angled triangle is a triangle with one angle greater than 90° but less than 180°.

• Feature: it has one obtuse angle.
• Other angles: the other two angles are acute.

What is an acute-angled triangle?

An acute-angled triangle is a triangle in which all three angles are acute.

• Feature: every angle is greater than 0° but less than 90°.
• Example: a triangle with angles 60°, 60° and 60°.

How do we find a missing angle?

A missing angle is found by subtracting the known angle from the total for that pair.

Example 1: complementary angles

Two angles are complementary. One is 35°. Find the other.

1. Write the rule: the sum is 90°.
2. Subtract: 90° – 35° = 55°.
3. The other angle is 55°.

Example 2: supplementary angles

Two angles are supplementary. One is 125°. Find the other.

1. Write the rule: the sum is 180°.
2. Subtract: 180° – 125° = 55°.
3. The other angle is 55°.

Evaluation

1. What is the measure of a straight angle?
2. State the range of values of ϴ for an obtuse angle and for a reflex angle.
3. What is the sum of two complementary angles? What is the sum of two supplementary angles?
4. What is the property of vertically opposite angles?
5. Describe an obtuse-angled triangle.

Assignment

1. Define adjacent angles.
2. Two angles are complementary. One of them is 40°. Find the other angle.
3. Two angles are supplementary. One of them is 120°. Find the other angle.
4. When are the angles formed by a transversal called corresponding angles, and how do their sizes compare?