What is an angle?

An angle is formed when two straight lines or rays meet at a common point called the vertex. The amount of rotation from one ray to the other is measured in degrees (°).

Parts: Vertex (where the rays meet) and arms or sides (the two rays).

Measuring angles

We measure angles using a protractor in degrees (°). A full turn is 360°, a half turn is 180°, and a right angle is 90°.

Types of angles (with simple diagrams)

Special angle relationships

• Complementary angles: Two angles add to 90°. Example: 30° and 60°.
• Supplementary angles: Two angles add to 180°. Example: 110° and 70°.
• Adjacent angles: Two angles with a common side and vertex (no overlap).
• Vertically opposite angles: When two lines cross, opposite angles are equal. (Example diagram below.)
• Linear pair: Two adjacent angles that form a straight line; they add to 180°.

Angle facts for triangles and at a point

- The sum of interior angles in any triangle is 180°. (So in a triangle with angles 50° and 60°, the third is 70°.)
- Angles at a point add up to 360°.
- Exterior angle of a triangle equals the sum of the two opposite interior angles.

Everyday examples (Kenya)

• Corner of a school book or blackboard — right angles (90°).
• Clock hands at 3 o’clock — right angle between hour and minute hand.
• Sloping roof angles on a house — acute or obtuse angles.

Practice Questions

1. Give the name (acute, right, obtuse, etc.) for each angle: 45°, 90°, 150°.
2. Two angles are complementary. One is 37°. Find the other.
3. Two lines cross. One angle is 110°. What is the vertically opposite angle?
4. In a triangle, two angles are 40° and 85°. Find the third angle.
5. Find x: If angle A and angle B are supplementary and A = 130°, what is B?