Virginia SOL Math / Geometry / Polygons & Circles

G.PC.2

Angles of Convex Polygons

What you'll learn

  • Find the sum of the interior angles of a convex polygon
  • Find one interior angle of a regular polygon
  • Use the fact that exterior angles sum to 360 degrees

Words to know

Convex polygon —
a polygon with no dents; all vertices point outward
Regular polygon —
a polygon with all sides and angles equal
Interior angle sum —
(n - 2) x 180 degrees for n sides
Exterior angle —
the angle outside the polygon at a vertex

Why it matters Interior-angle rules let designers of tiles, gears, and geodesic domes make shapes fit together perfectly around a point.

Worked examples

Model ItI do

Find the sum of the interior angles of this convex pentagon.

Use the sum formula (n - 2) x 180 with n = 5: (5 - 2) x 180 = 3 x 180 = 540 degrees.

Try It TogetherWe do

Find the measure of one interior angle of a regular hexagon.

First the sum: (6 - 2) x 180 = 720 degrees. A regular hexagon has 6 equal angles, so each is 720 / 6 = 120 degrees.

Now YouYou do

What is the measure of one exterior angle of a regular octagon?

Exterior angles of any convex polygon sum to 360 degrees; divide by the number of sides. Check your answer in the back of this chapter.

Practice

Mastered 0 of 11

Warm-up

Ease in with the basics.

  1. 1.Find the sum of the interior angles of a hexagon.

  2. 2.The exterior angles of any convex polygon total how many degrees?

  3. 3.Find one exterior angle of a regular hexagon.

On Level

The core Quick Check from the book.

  1. 1.Find the interior angle sum of a hexagon.

  2. 2.How many degrees do the exterior angles of any convex polygon total?

  3. 3.Find one interior angle of a regular pentagon.

  4. 4.A polygon's interior angles sum to 1080 degrees. How many sides does it have?

  5. 5.Find one exterior angle of a regular hexagon.

Challenge

Stretch your thinking.

  1. 1.The interior angles of a convex polygon sum to 1440 degrees. How many sides does it have?

  2. 2.Find the measure of one interior angle of a regular octagon.

  3. 3.A regular polygon has an exterior angle of 24 degrees. How many sides does it have?