Types of Angles

An angle is the amount of turn between two lines that meet at a point (called the vertex). We measure angles in degrees (the symbol is °).

Acute Angle

Less than 90°

Right Angle

Exactly 90°

Obtuse Angle

Between 90° and 180°

Straight Angle

Exactly 180°

Reflex Angle

Between 180° and 360°

Full Turn

Exactly 360°

Measuring Angles with a Protractor

Step 1: Place the protractor's centre point on the angle's vertex.

Step 2: Line up the baseline with one arm of the angle.

Step 3: Read the scale where the other arm crosses. This angle is 50°.

Angles in a Triangle

The three angles inside any triangle always add up to 180°. This is one of the most important rules in geometry.

70° + 60° + 50° = 180°

The angles in a triangle always sum to 180°.

Finding a Missing Angle

If you know two angles, subtract their sum from 180° to find the third.

Example: A triangle has angles of 90° and 35°. Find the third angle.

Step 1: Add the known angles: 90 + 35 = 125°

Step 2: Subtract from 180°: 180 - 125 = 55°

Properties of Quadrilaterals

A quadrilateral is any shape with exactly 4 straight sides. The angles in a quadrilateral always add up to 360°.

Square

4 equal sides
4 right angles (90°)
2 pairs of parallel sides

Rectangle

2 pairs of equal sides
4 right angles (90°)
2 pairs of parallel sides

Parallelogram

2 pairs of equal sides
Opposite angles are equal
2 pairs of parallel sides

Rhombus

4 equal sides
Opposite angles are equal
2 pairs of parallel sides

Trapezium

1 pair of parallel sides
Side lengths can all differ

Kite

2 pairs of adjacent equal sides
1 pair of opposite equal angles
No parallel sides

Key Vocabulary

Angle

The amount of turn between two lines meeting at a point. Measured in degrees (°).

Vertex

The point where two lines (or edges) meet to form an angle.

Protractor

A tool used to measure and draw angles.

Parallel

Lines that are always the same distance apart and never meet.

Worked Examples

1

Classify an angle of 135°.

Step 1: Is it less than 90°? No.

Step 2: Is it exactly 90°? No.

Step 3: Is it between 90° and 180°? Yes!

Answer: 135° is an obtuse angle.

2

A triangle has angles of 40° and 80°. Find the missing angle.

Step 1: Add known angles: 40 + 80 = 120°

Step 2: Subtract from 180°: 180 - 120 = 60°

Answer: The missing angle is 60°.

3

Three angles of a quadrilateral are 90°, 90° and 110°. Find the fourth.

Step 1: Add known angles: 90 + 90 + 110 = 290°

Step 2: Subtract from 360°: 360 - 290 = 70°

Answer: The fourth angle is 70°.

Knowledge Check

Select the correct answer for each question. Click "Check Answer" to see if you are right.

Question 1

What type of angle is 72°?

Obtuse Acute Right Reflex

Question 2

A triangle has angles of 50° and 60°. What is the third angle?

110° 80° 70° 90°

Question 3

How many degrees are in a straight angle?

90° 360° 270° 180°

Question 4

Which quadrilateral has 4 equal sides but does NOT have to have right angles?

Rhombus Rectangle Square Trapezium

Question 5

What do the angles in a quadrilateral add up to?

180° 360° 270° 400°

Angles & Shapes