l3-4: angles of polygons warmup: draw and write the name of as many shapes as you can like the ones...
TRANSCRIPT
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