L3-4: Angles of L3-4: Angles of PolygonsPolygonsWarmup:

Draw and write the name of as many shapes as you can like the ones below

PolygonsPolygons .. ..

A B

C

DE

F

Convex vs. ConcaveConvex vs. Concave

Convex PolygonConvex Polygon

Concave PolygonConcave Polygon

Convex Polygon Concave Polygon

Number of SidesNumber of Sides PolygonPolygon

33

44

55

66

77

88

99

1010

1111

1212

NN

Regular PolygonsRegular Polygons

Regular:Regular:

Activity - Polygons & Angles

In the following tableDraw each figure – regular polygonsDraw as many non-overlapping triangles inside

each figureUse facts of angles in triangles and

supplementary angles to finish the table.

Complete the following table

# of sides

Drawing (regular) # of ∆’s

Sum of interior angles

(∆’s * 180)

Each interior angle (regular)

Each exterior angle (regular)

Sum of exterior angles

3

4

5

6

n n sides n – 2 (n – 2)●180 n

n 180)2( 360/n 360

# of sides

Drawing (regular) # of ∆’s

Sum of interior angles

(∆’s * 180)

Each interior angle (regular)

Each exterior angle (regular)

Sum of exterior angles

8

Example

Most Useful Equations:

Examples:

1) Name the figure below

2) Find the measure of an exterior angle in a regular pentagon.

3) Find the name of a regular polygon with interior angles equal to 1200.

The measure of an interior angle of a regular polygon is 144. Find the number of sides in the polygon.

1) Interior angle = 144, then exterior angles = 180 – 144 = 36

2) Exterior angles must add to 360: 36 * n = 360

3) n = 10

Example 4

Find the measure of each interior angle.

4 sides: angles add to 360!

Example 5

Find the measures of an exterior angle and an interior angle of convex regular hexagon ABCDEF.

Exterior angles: 360 / 6 sides = 600 each

Interior angles: supplementary to exterior 180 – 60 = 1200

Example 6