Grade 6 Mathematics Geometry – Angles Notes
Mathematics — Geometry: Angles
Age: 11 (Kenyan Primary level) — Short notes and simple drawings to help you learn what angles are, how to measure them, and different kinds of angles.
Learning goals
- Know the parts of an angle (vertex and arms).
- Recognise different types of angles (acute, right, obtuse, straight, reflex, full).
- Measure and draw angles using a protractor.
- Understand complementary, supplementary, adjacent and vertically opposite angles.
What is an angle?
An angle is made when two straight lines or rays meet at a point. The point is called the vertex. Each straight line is called an arm or ray.
Parts:
- Vertex — the corner point where arms meet.
- Arms (rays) — the straight lines from the vertex.
How we write an angle
Use the symbol ∠. Example: ∠AOB means the angle made by rays OA and OB with vertex at O.
Types of angles
Acute angle
Less than 90°. Example: angle of 60°.
Less than 90°. Example: angle of 60°.
Right angle
Exactly 90°. Example: the corner of a book or clock at 3 o'clock.
Exactly 90°. Example: the corner of a book or clock at 3 o'clock.
Obtuse angle
More than 90° and less than 180°. Example: 120°.
More than 90° and less than 180°. Example: 120°.
Straight angle
Arms point in opposite directions — equals 180° (a straight line).
Arms point in opposite directions — equals 180° (a straight line).
Reflex angle
Greater than 180° and less than 360°.
Full angle
360° — a full turn.
Greater than 180° and less than 360°.
Full angle
360° — a full turn.
Special angle pairs
- Complementary angles: two angles whose sum is 90°. (e.g., 30° and 60°)
- Supplementary angles: two angles whose sum is 180°. (e.g., 110° and 70°)
Adjacent angles share a common arm and vertex (e.g., angles 1 and 2).
Vertically opposite angles are equal (e.g., angle 1 = angle 3).
Vertically opposite angles are equal (e.g., angle 1 = angle 3).
Measuring angles with a protractor — simple steps
- Place the protractor so its centre hole (or midpoint) is on the vertex.
- Make sure one arm lines up with the zero line on the protractor.
- Read the number on the protractor where the other arm crosses the curved edge.
- Use the inner or outer scale correctly (start from 0 on correct side).
How to draw an angle of, say, 60°
- Draw a straight line and mark the vertex O.
- Place protractor centre on O and mark a point at 60°.
- Join O to that point — the angle is 60°.
Practice exercises
- Identify the type of these angles: 30°, 90°, 150°, 180°, 300°.
- Two angles are complementary. One is 35°. What is the other?
- Two angles are supplementary. One is 125°. What is the other?
- In crossing lines, angle 1 = 40°. What is the size of the vertically opposite angle? What is the adjacent angle?
- Draw a 45° angle using the steps above (use a protractor).
- Real-life: The hands of a clock are at 4:00. Is the angle between them acute, right, or obtuse? (Hint: each hour is 30°)
Answers (click to show)
- 30° — acute; 90° — right; 150° — obtuse; 180° — straight; 300° — reflex.
- Complementary sum to 90° → other = 90° − 35° = 55°.
- Supplementary sum to 180° → other = 180° − 125° = 55°.
- Vertically opposite angle = 40°. Adjacent angle = 180° − 40° = 140°.
- Answer depends on drawing; check with a protractor to ensure the angle reads 45°.
- At 4:00, difference = 4 × 30° = 120°, so the angle is obtuse (120°).
Tips: Practice with a real protractor and a ruler. Try finding angles around your classroom — clock hands, book corners, doors and window frames are useful examples.
For Kenyan learners: These concepts appear in primary upper basic mathematics (CBC). Practise with past exam-style questions and ask your teacher for extra worksheets if you need more practice.