How many sides, from the turn at a corner

Difficulty Stretch · Set t8blit

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1
Walking once round a regular shape, the turn at each corner is 120°. How many sides has it?
2
Walking once round a regular shape, the turn at each corner is 36°. How many sides has it?
3
Walking once round a regular shape, the turn at each corner is 45°. How many sides has it?
4
Walking once round a regular shape, the turn at each corner is 40°. How many sides has it?
5
Walking once round a regular shape, the turn at each corner is 90°. How many sides has it?
6
Walking once round a regular shape, the turn at each corner is 30°. How many sides has it?
7
Walking once round a regular shape, the turn at each corner is 90°. How many sides has it?
8
Walking once round a regular shape, the turn at each corner is 40°. How many sides has it?
9
Walking once round a regular shape, the turn at each corner is 30°. How many sides has it?
10
Walking once round a regular shape, the turn at each corner is 45°. How many sides has it?
11
Walking once round a regular shape, the turn at each corner is 72°. How many sides has it?
12
Walking once round a regular shape, the turn at each corner is 45°. How many sides has it?
13
Walking once round a regular shape, the turn at each corner is 60°. How many sides has it?
14
Walking once round a regular shape, the turn at each corner is 90°. How many sides has it?
15
Walking once round a regular shape, the turn at each corner is 60°. How many sides has it?
16
Walking once round a regular shape, the turn at each corner is 120°. How many sides has it?
17
Walking once round a regular shape, the turn at each corner is 36°. How many sides has it?
18
Walking once round a regular shape, the turn at each corner is 40°. How many sides has it?
19
Walking once round a regular shape, the turn at each corner is 90°. How many sides has it?
20
Walking once round a regular shape, the turn at each corner is 90°. How many sides has it?

What is in this set

The numbers in this set run from 30 to 120.
Every problem in it will use a shape whose angles are all the same.
A careful solution takes 2 written steps on average.
The mistake this set invites most often, in 100% of the problems: the turns add to 360° all the way round, so the number of them is 360 divided by one turn.
Answers are a whole number.

Drawing 240 problems from this page produced 8 different ones, 3% — so a sheet of 20 will come back to a problem you have seen — there are only so many sensible ones of this kind.

The same skill, harder or easier

We would put this in front of a grade 8 class. That is our judgement, not a standard, and it is printed here so you can disagree with it. Everything else we put in that year.