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

Recall / Warm-Up

Review what makes a polygon regular before working with angle sums.

$A square with equal sides and equal angles beside a rectangle with equal angles but unequal side lengths$

A rectangle has all four angles equal ( $90\degree$ each) but its sides are not all equal (two long, two short). Is a rectangle a regular polygon?

Yes — having all angles equal is enough on its own to make a polygon regular, regardless of what the side lengths happen to be, since the angle condition is treated as the defining one

No — a regular polygon needs both all sides equal AND all angles equal; the rectangle fails the equal-sides condition even though its angles are equal

No — a regular polygon needs all sides equal, but the angles do not need to match at all, since side length is treated as the only condition that determines regularity