Geometry Section 5.1

Polygons &

their angle measures

Learning Target:I can calculate angle measure for angles of polygons. [G.MG.1]

Activity: Exploring the Sum of the Interior and Exterior Angles of convex polygons

4

5

6

7

8

4

5

6

7

8

2

3

4

5

6

180˚

180˚180˚

180˚

180˚

180˚

360˚540˚

720˚

900˚

1080˚

POLYGON INTERIOR ANGLES THEOREMThe sum of the measures of the interior angles of a convex polygon with n sides is

POLYGON EXTERIOR ANGLES THEOREMThe sum of the measures of the exterior angles of a convex polygon, one angle at each vertex, is ________.

m∠1 + m∠2 + m∠3 + m∠4 + m∠5 = 360

http://www.mathsisfun.com/geometry/exterior-angles-polygons.html

SUM Interior ∠s = (n – ___ ) _______

SUM Exterior ∠s = ______

2) The sum of the interior angles of a polygon is 1980˚, classify the polygon by the number of sides.

1) Find the sum of the interior angles of

b) 15-gona) decagon

xo

(x + 20)˚

112˚96o

4) Find the value of x.

3) Find the value of x. Hint: find the sum of the interior angles first

Hint: find the sum of the exterior angles first

5) Find the measure of one interior ∠ AND one exterior ∠ on a stop sign.

6) Each interior angle of the regular n-gon has a measure is 162˚. Find the value of n.

OR

Homework:5.1 Angles in Polygons

Sum Interior = (n – 2) • 180

Sum Exterior = 360˚

In a Regular Polygon

Each Interior =n

(n – 2) •180

Each Exterior = n 360

Assignment: 5.1 worksheet