Transcript Unit 3 Comp 4B

Interior/Exterior Angles
in Regular Polygons
R.4.G.2 Solve problems using properties of polygons:
sum of the measures of the interior angles of a polygon
interior and exterior angle measure of a regular polygon or irregular polygon
number of sides or angles of a polygon
Regular Polygon: a polygon with all congruent sides
and all congruent angles
Diagonal: a line drawn through the interior of a polygon
from a vertex to a non-consecutive vertex.
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
Octagon
Polygon
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
Number
of Sides
Number of triangles
formed by drawing all
diagonals from one
vertex
Sum of
angle
measures
in each
triangle
The sum of the
interior angles
Polygon
Octagon
Nonagon
Decagon
N-gon
20-gon
Number
of Sides
Number of triangles
formed by drawing all
diagonals from one
vertex
Sum of
angle
measures
in each
triangle
The sum of the
interior angles
The sum of the measures of the
interior angles of an n-gon is
180(n-2)
Find the sum of the interior angles of the following
polygons:
Dodecagon
18-gon
 Draw an exterior angle at each vertex of the polygons.
 Measure each exterior angle and find the sum of all the
exterior angles for each polygon. Record your results
in the table.
Polygon
Triangle
Quadrilateral
Pentagon
Hexagon
n-gon
20-gon
Number of Sides
Measures of one
Exterior Angle
Sum of the
Measures of
the Exterior
Angles
The sum of the exterior angles
of any polygon is
360 degrees!
To find one exterior angle of any polygon with “n” sides:
360
n
Interior Angle + Exterior Angle = 180o
Find the measure of each interior and exterior angle of a
regular octagon.
n= 8
Exterior angle = 45o
Interior angle = 135o
Find the measure of each interior and exterior angle of a
22-gon.
Interior: 163.6o
Exterior: 16.4o
If the exterior angle measures 40o in a regular polygon,
how many sides does it have?
If the exterior angle measures 120o in a regular polygon,
how many sides does it have?
xo
xo
55o
2xo
(x+10)o
(3x-17)o
(x+10)o
xo
yo