Back to Polygons: Properties, Construction, and Angle Sums — Problem 1 · Task Set 29

Exercises: Polygons, Construction, and Angle Sums

Use the interior angle sum formula $(n-2) \times 180\degree$ and remember: dividing by $n$ to get a single angle only works for regular polygons.

Grade 7·16 problems·~25 min·Uganda NCDC Primary 7 Mathematics·lesson·construction-03

Work through problems with immediate feedback

Fluency Practice

$A near-hexagon formed by stepping points around a circle, with a small gap where the sixth mark misses the starting point$

You are constructing a regular hexagon by stepping a circle's radius six times around its circumference, but midway through you accidentally widen the compass slightly. What happens?

Nothing — the hexagon still closes exactly, since only the very last of the six steps actually needs to use the correct, unchanged radius

The sixth mark misses the starting point, because the stepping radius no longer matches the circle's radius for every step

The hexagon still closes, but the shape it forms becomes a regular pentagon instead of a hexagon, since one step effectively merges with another