CK-12 Geometry Concepts

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

MEDIA

Click image to the left for more content.

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◦.

Vocabulary

Theinterior angleof a polygon is one of the angles on the inside. Aregular polygonis a polygon that isequilateral
(has all congruent sides) andequiangular(has all congruent angles).

Guided Practice

1. Find the measure ofx.


2. The interior angles of a pentagon arex◦,x◦, 2 x◦, 2 x◦,and 2x◦. What isx?


3. What is the sum of the interior angles in a 100-gon?

Answers:

1. From the Polygon Sum Formula we know that a quadrilateral has interior angles that sum to( 4 − 2 )× 180 ◦= 360 ◦.

Write an equation and solve forx.

89 ◦+( 5 x− 8 )◦+( 3 x+ 4 )◦+ 51 ◦= 360 ◦

8 x= 224

x= 28

2. From the Polygon Sum Formula we know that a pentagon has interior angles that sum to( 5 − 2 )× 180 ◦= 540 ◦.

Write an equation and solve forx.

x◦+x◦+ 2 x◦+ 2 x◦+ 2 x◦= 540 ◦

8 x= 540

x= 67. 5

3. Use the Polygon Sum Formula.( 100 − 2 )× 180 ◦= 17 , 640 ◦.

Practice

1. Fill in the table.