Warm-up
Three quick questions from earlier lessons.
Discover
A triangle's angles add up to 180°. What do a quadrilateral's angles add up to?
- 360°
- 180°
Key idea
Interior angles come from triangles; exterior angles always total 360°.
From one vertex, diagonals split an -sided polygon into triangles, so its interior angles add up to . Walking around any convex polygon you turn through 360° in all: the exterior angles add up to 360°. In a regular polygon all of them are equal.
Worked example
A regular hexagon.
Interior sum.
Each interior angle.
Each exterior angle.
Your turn, guided
Your turn: the interior angle sum of a pentagon.
(5 − 2) · 180.
Practice ★
- What is the sum of the interior angles of a polygon with 12 sides, in degrees?
- What is the sum of the interior angles of a polygon with 9 sides, in degrees?
- Each exterior angle of a regular polygon with 3 sides measures how many degrees?Not to scale
Watch out!
Practice ★★
- The interior angles of a polygon add up to 720°. How many sides does the polygon have?
- The interior angles of a polygon add up to 900°. How many sides does the polygon have?
- Each exterior angle of a regular polygon with 3 sides measures how many degrees?Not to scale
Exit ticket
Three questions to check you have got it.
- What is the sum of the interior angles of a polygon with 12 sides, in degrees?
- What is the sum of the interior angles of a polygon with 9 sides, in degrees?
- What is the sum of the interior angles of a polygon with 6 sides, in degrees?
Summary card
Polygon angles
Interior sum (n − 2) · 180°; exterior sum 360°.
Watch out: n − 2 triangles, not n.