GRADE 6 · MATHEMATICS

Angles and Triangles

Angles describe turns and the space between two lines or rays. Learn common angle types, how to measure an angle with a protractor, how triangles are classified and why the angles inside every triangle add up to 180°.

Learning time: approximately 30 minutes · Beginner level

What You Will Learn

Identify acute, right, obtuse, straight and reflex angles.
Measure angles using a protractor.
Classify triangles by their sides and angles.
Use the 180° angle sum of a triangle to find a missing angle.
Recognise angles on a straight line and around a point.

1. What Is an Angle?

An angle is formed when two rays or line segments meet at a common endpoint called the vertex. The amount of turn between them is measured in degrees (°).

Angles are measured in degrees.

One full turn = 360° · Half a turn = 180° · A quarter turn = 90°

2. Types of Angles

AcuteGreater than 0° and less than 90°

RightExactly 90°

ObtuseGreater than 90° and less than 180°

StraightExactly 180°

ReflexGreater than 180° and less than 360°

Full turnExactly 360°

Examples: 35° is acute, 90° is right, 125° is obtuse, 180° is straight and 240° is reflex.

3. Measure an Angle with a Protractor

Place the centre mark of the protractor exactly on the angle's vertex.
Line up the baseline of the protractor with one arm of the angle.
Look at the scale that starts at 0° on the arm you lined up.
Read the number where the other arm crosses the scale.
Check whether the answer makes sense: is the angle acute, right or obtuse?

Common mistake: A protractor often has two scales. Start reading from the 0° mark on the side aligned with the first arm. Do not choose the other scale by mistake.

4. Classify Triangles by Their Sides

Triangle	Side lengths	Key property
Equilateral	All three equal	All angles are 60°
Isosceles	At least two equal	Angles opposite the equal sides are equal
Scalene	All different	All side lengths are different

5. Classify Triangles by Their Angles

Triangle	Angle property
Acute-angled	All three angles are less than 90°
Right-angled	One angle is exactly 90°
Obtuse-angled	One angle is greater than 90°

A triangle cannot have two right angles or two obtuse angles because its interior angles must add up to 180°.

6. The Angle Sum of a Triangle

The three interior angles of every triangle add up to 180°.

A + B + C = 180°

Worked example: Find the missing angle

A triangle has angles of 50° and 60°. Find the third angle.

Add the known angles: 50° + 60° = 110°.
Subtract from 180°: 180° − 110° = 70°.

The missing angle is 70°.

Another example

A triangle has angles 90° and 35°. The third angle is 180° − 90° − 35° = 55°.

7. Angles on a Straight Line and Around a Point

Angles on a straight line add up to 180°.
Angles around a point add up to 360°.
Vertically opposite angles are equal when two straight lines cross.

Example: If two angles on a straight line are 125° and x, then x = 180° − 125° = 55°.

8. Common Mistakes to Avoid

Reading the wrong protractor scale: Start at the 0° mark aligned with the first arm.

Thinking every triangle has equal angles: Only an equilateral triangle has three equal angles.

Forgetting the triangle total: Interior angles of a triangle always add to 180°.

Confusing side and angle names: A right-angled triangle has one 90° angle; it does not need equal sides.

9. Practice Exercises

Try these before revealing the answers.

Classify an angle of 42°.
Classify an angle of 135°.
How many degrees are in a straight angle?
Two angles in a triangle are 45° and 65°. Find the third angle.
A triangle has angles 90° and 28°. Find the third angle.
What is the total of angles around a point?
What type of triangle has all three equal sides?

Show practice answers and explanations

Acute angle.
Obtuse angle.
180°.
180° − 45° − 65° = 70°.
180° − 90° − 28° = 62°.
360°.
Equilateral triangle.

11. Free Printable Worksheet

Print this worksheet or save it as a PDF for extra practice.

Learnora — Grade 6 Mathematics