In short: A hard angle puzzle is really several small steps. Mark everything you know first, then look for a triangle, a straight line or a point where only one angle is missing, and give a reason for each angle you find.
Before you start
You need every rule from this unit. Here they are in one place:
| Rule | Fact |
|---|---|
| Straight line | angles add to |
| Around a point | angles add to |
| Vertically opposite | equal |
| Triangle | angles add to |
| Exterior angle of a triangle | equals the two opposite inside angles added |
| Isosceles triangle | base angles are equal |
| Equilateral triangle | every angle is |
| Quadrilateral | angles add to |
| Parallel lines | corresponding and alternate angles equal, co-interior add to |
The detective method
Worked puzzles
Angle puzzles
Method
- Mark what you know
- Find a shape with one gap
- Write angle and reason
- Repeat
Favourite clues
- Tick marks: isosceles
- Arrows: parallel
- Straight line: 180°
Traps
- Not to scale
- Reflex vs inside angle
Quick summary
- Big angle problems are several small steps.
- Mark everything you know first, including equal sides and parallel lines.
- Find a triangle, straight line or point with only one angle missing.
- Write each new angle with its reason.
- Tick marks almost always mean "use the isosceles rule".
- Never trust how a diagram looks if it says "not to scale".
Quiz
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Try 3 questions now
Points , , are on a straight line. Angle . What is angle ?
- A
- B
- C
- D
Show answer
B:
Straight line: .
A triangle has angles and . What is the third?
- A
- B
- C
- D
Show answer
A:
.
Two sides of a triangle have tick marks. The angle between them is . What is each of the other angles?
- A
- B
- C
- D
Show answer
C:
Isosceles: .