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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
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PolygonsPolygons .. ..
A B
C
DE
F
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Convex vs. ConcaveConvex vs. Concave
Convex PolygonConvex Polygon
Concave PolygonConcave Polygon
Convex Polygon Concave Polygon
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Number of SidesNumber of Sides PolygonPolygon
33
44
55
66
77
88
99
1010
1111
1212
NN
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Regular PolygonsRegular Polygons
Regular:Regular:
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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.
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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
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# 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
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Most Useful Equations:
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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.
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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
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Find the measure of each interior angle.
4 sides: angles add to 360!
Example 5
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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