Discover Mathematics P4: Term 2, Unit 13, Lessons 1–4
GoalFind the size of an angle at the centre of a circle cut into equal parts, using the benchmarks 45°, 90°, 135° and 180°.
New words
centre of a circle · the point in the middle, the same distance from every point on the circlebenchmark angle · an angle we know well, such as 45°, 90°, 135° or 180°, used to estimate other anglesequal parts · parts of the same size
Explanation
Many angles have their vertex at the centre of a circle. A whole circle makes a full turn of 360°. If a circle is cut into equal slices, every slice has the same angle at the centre. For 8 equal slices, each angle is 360° ÷ 8 = 45°. Then 2 slices make 2 × 45° = 90° (a right angle), 3 slices make 135° and 4 slices make 180° (a straight angle). These four angles are benchmarks: if we know them, we can compare any angle with them. An angle between 45° and 90° is acute, between 90° and 135° is obtuse, and so on. To find the angle of some slices, multiply the number of slices by the angle of one slice.
Worked examples
A round tray of kunafa is cut into 8 equal slices. The angle of one slice at the centre is 360° ÷ 8 = 45°. Check: 8 × 45° = 360°.
Salma eats 3 slices of the 8. The angle of the part she ate is 3 × 45° = 135°. The part left is 5 slices: 5 × 45° = 225°. Check: 135° + 225° = 360°.
Use the benchmarks. 2 slices make 90°, which is a right angle. 4 slices make 180°, a straight angle. An angle with 1 slice is 45°, half of a right angle. These benchmark angles help us estimate: an angle a bit wider than 90° but narrower than 135° is obtuse.
Class activity
Make a protractor from paper. Cut a circle from paper and fold it in half, then in half again, then in half again so that you have 8 equal parts. Open it and mark the centre. Write 45°, 90°, 135° and 180° on the folds. Use your paper circle to compare angles from your room: is each one smaller or larger than 90°?
Practice
1
A circle is cut into 6 equal parts. What is the angle of each part at the centre?
360° ÷ 6 = 60°.
2
An angle covers 2 slices of an 8-slice circle. How many degrees is it?
2 × 45° = 90°.
3
Mina eats 3 of the 8 equal slices of a round pie. What is the angle of the part that is left?
