Angles
Angle facts, triangles, parallel lines and polygons
Angles measure turn. A full turn is 360°, and a few simple facts let you find any missing angle.
Angle facts
- Angles on a straight line add up to 180°.
- Angles around a point add up to 360°.
- Angles in a triangle add up to 180°; in a quadrilateral, 360°.
- Vertically opposite angles are equal.
- Parallel lines: alternate angles are equal (Z shape) and corresponding angles are equal (F shape).
- Exterior angles of any polygon add up to 360°. Interior angles of an n-sided polygon add up to (n − 2) × 180°.
Types: acute (less than 90°), right (90°), obtuse (between 90° and 180°), reflex (more than 180°).
Worked examples
Example 1. Two angles on a straight line: one is 125°. Find the other.
Example 2. A triangle has angles 48° and 67°. Find the third angle.
Example 3. Find the interior angle of a regular hexagon.
Top tips and common mistakes
- Give reasons, like “angles on a straight line add up to 180°”. Exams award marks for them.
- An isosceles triangle has two equal angles.
- Use the inside scale of a protractor when your angle starts on the right.
I spot angles everywhere now: in roofs, ramps and even pizza slices!
Practise
Answer as many as you like. Every question is new, and you get a “correct” tick for each one you get right first time. Use “Show answer” to see a worked solution.
Quiz: earn your stamp
Printable worksheet
Angles worksheet. The questions come first and the answers for grown-ups are on the last page, so you can print just the question pages.
Printing is optional. A4 size.