Word problems about angles and circles
These problems use what you know about angles and circles in real life, such as turns you make when walking, the corners of shapes, and round objects like wheels and tables. First read the problem and decide whether it is about a straight line, a point, or a circle. Then use four steps: understand the story, plan the calculation, solve it carefully, and check the answer.
Key idea
Angles on a line add to 180°. Angles at a point add to 360°. For circles, diameter = 2 × radius.
A worked problem
Worked example
Three angles meet at the centre of a fan: 90°, 130° and one more. What is the third angle? Angles at a point make 360°, so 360 − 90 − 130 = 140°. Check: 90 + 130 + 140 = 360°. Correct!
Remember
- Choose 180° for a straight line, 360° for a point.
- A round object: diameter = twice the radius.
- Always check your total.
- Decide first whether the picture shows a straight line, a point, or a circle before you calculate.