How it works
This polygon quiz has 42 questions in two sets: the name of each polygon from its number of sides, from the triangle to the dodecagon, and the sum of the interior angles and one angle of a regular polygon.
Read the full guide
Two sets
Name the polygon asks both ways, the name for a number of sides and the number of sides for a name, and adds regular, convex and concave. Angle sums and regular polygons goes from the sum to one interior angle, exterior angles and a missing angle.
- An interior angle and the exterior angle at the same vertex add up to 180°, so a 120° interior angle means a 60° exterior angle.
- Equal sides alone do not make a polygon regular: a rhombus has four equal sides, but it is regular only when it is a square.
Questions and answers
What are the names of polygons by number of sides?
3 triangle, 4 quadrilateral, 5 pentagon, 6 hexagon, 7 heptagon, 8 octagon, 9 nonagon (or enneagon), 10 decagon, 11 hendecagon (or undecagon) and 12 dodecagon. A polygon with n sides is also called an n-gon, so one with 13 sides is a 13-gon.
How do you find the sum of the interior angles of a polygon?
Subtract 2 from the number of sides and multiply by 180°. A hexagon has 6 sides, so its interior angles add up to (6 − 2) × 180° = 720°.
How do you find one interior angle of a regular polygon?
Find the angle sum and divide by the number of sides, because all the angles are equal. A regular octagon has a sum of 1080°, so each angle is 1080° ÷ 8 = 135°.
What is the sum of the exterior angles of a polygon?
360° for any convex polygon, counting one exterior angle at each vertex, whatever the number of sides. A regular dodecagon has 12 exterior angles of 30° each.