CK-12 Geometry-Concepts

6.1. Interior Angles in Convex Polygons http://www.ck12.org

Aregular polygonis a polygon where all sides are congruent and all interior angles are congruent.

Regular Polygon Formula:For anyequiangularn−gon, the measure of each angle is(n−^2 )×^180

◦

n.

Example A

Find the sum of the interior angles of an octagon.

Use the Polygon Sum Formula and setn=8.

( 8 − 2 )× 180 ◦= 6 × 180 ◦= 1080 ◦

Example B

The sum of the interior angles of a polygon is 1980◦. How many sides does this polygon have?

Use the Polygon Sum Formula and solve forn.

(n− 2 )× 180 ◦= 1980 ◦

180 ◦n− 360 ◦= 1980 ◦

180 ◦n= 2340 ◦

n= 13 The polygon has 13 sides.

Example C

How many degrees does each angle in an equiangular nonagon have?

First we need to find the sum of the interior angles in a nonagon, setn=9.

( 9 − 2 )× 180 ◦= 7 × 180 ◦= 1260 ◦

Second, because the nonagon is equiangular, every angle is equal. Dividing 1260◦by 9 we get each angle is 140◦.

Watch this video for help with the Examples above.

MEDIA

Click image to the left for use the URL below.

URL: http://www.ck12.org/flx/render/embeddedobject/52569

CK-12 Foundation: Chapter6InteriorAnglesinConvexPolygonsB

Concept Problem Revisited

A regular polygon has congruent sides and angles. A regular hexagon has( 6 − 2 ) 180 ◦= 4 · 180 ◦= 720 ◦total
degrees. Each angle would be 720◦divided by 6 or 120◦.