FMath 11
2.4 Angle Properties In Polygons
A polygon is a closed geometric figure made up of n straight sides.
A convex polygon has all interior angles less
than 180°.
# of sides in a
polygon
sketch
A concave polygon has at least one interior
angle greater than 180°.
# of triangles
formed
Sum of interior angles
of the polygon
3
1
1×180° =180°
4
2
2×180° =360°
5
6
7
8
9
10
11
12
n
In any polygon with n sides, the sum of the interior angles is 180(n-2)
A regular polygon has equal sides and equal angles.
Example 1:
Determine the measure of each interior angle of a regular 17-sided polygon.
Exterior and Interior Angles:
Example 2:
Show that the sum of the exterior angles of a pentagon is 360°.
1. Draw a pentagon (5 sided)
2. Figure out the sum of the interior
angles
3. Find the measure of each interior angle
4. Find the measure of the exterior
angles
5. Add up the measures of the exterior
angles
Theorem : The sum of the exterior angles of any convex polygon is 360°.
Show that each exterior angle of a regular polygon is
360
.
n
1. Draw an octagon (8 sided), hexagon (6 sided), and a pentagon (5 sided). Then add on
the exterior angles in each polygon
Octagon
Hexagon
Pentagon
2. Find the sums of the interior angles for each
Octagon
Hexagon
3. Find the measure of the interior angles for each
Octagon
Hexagon
Pentagon
Pentagon
4. Find the measure of the exterior angles for each
Octagon
Hexagon
Pentagon
5. Find the answer to 360 divided by the number of sides for each polygon
Octagon
Hexagon
Pentagon
6. Compare the results in step 5 to the
results in step 4
Example 3:
7. List your observations of the results
from step 6
What type of regular polygon has an interior angle 3 times the exterior angle?
Example 4: A floor tiler designs custom floors using tiles in the shape of regular polygons.
Can the tiler use regular hexagons and equilateral triangles to tile a floor that have the same
side length?
Assignment: pg. 99 #1-4, 6-11, 14, 18