L3-4: Angles of Polygons Warmup: Draw and write the name of as many shapes as you can like the ones below

Polygons ........ AB C DE F

Convex vs. Concave  Convex Polygon  Concave Polygon Convex PolygonConcave Polygon

Number of Sides Polygon N

Regular Polygons  Regular:

Activity - Polygons & Angles In the following table  Draw each figure – regular polygons  Draw as many non-overlapping triangles inside each figure  Use 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 n n sidesn – 2 (n – 2)● /n360

# 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

Example 1-2b 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

Example 1-3d Find the measure of each interior angle. 4 sides: angles add to 360! Example 5

Example 1-4c Find the measures of an exterior angle and an interior angle of convex regular hexagon ABCDEF. Exterior angles: 360 / 6 sides = 60 0 each Interior angles: supplementary to exterior 180 – 60 = Example 6