Angles in polygons and symmetry
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The teaching part (1 min) is free to watch. A free account opens the whole lecture: 6 practice questions, 1 real past-paper question with the answer explained, the mistakes that lose marks, the full-marks tip, a one-card summary and a quick quiz.
What this lecture covers
- Honeycomb and stop signs
- Interior angles
- Regular polygons
Read the transcript of the teaching part
Last time
Before we start: last time, in Angles on lines, in triangles and quadrilaterals, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.
Honeycomb and stop signs
A honeycomb is built from hexagons, and a stop sign is an octagon. Both are regular polygons: every side equal, every angle equal. Once you know how many sides, you can find any angle. Then we turn to symmetry, the other way these shapes repeat themselves.
Interior angles
Split a polygon into triangles from one corner. An n-sided polygon makes n minus two triangles. Each triangle has one eighty degrees. So the interior angle sum is n minus two, times one eighty. A hexagon, six sides, has four triangles: seven hundred and twenty degrees.
Regular polygons
In a regular polygon, every interior angle is the same. Divide the sum by n. A regular hexagon: seven twenty over six is one hundred and twenty degrees. A regular octagon: ten eighty over eight is one thirty-five. A regular pentagon: five forty over five is one oh eight.
How often it comes up
How often Cambridge has asked each part, counted by ExamYard from every past paper in its question bank: Symmetry.
The whole chapter: Angles, Polygons and Symmetry.
Chapter 21: Angles and symmetry
- Angles on lines, in triangles and quadrilaterals 6 min
- Angles in polygons and symmetry 6 min
Also for O Level Maths 4024
Which topics come up most in O Level Maths 4024 past papers, counted from every paper since 2004.