Warm Up
1. A three sided polygon is called a __________.
2. A four sided polygon is called a ___________.
3. A five sided polygon is called a ___________.
4. The angles in a three sided polygon add up to
________ degrees.
5. The angles in a four sided polygon add up to
________ degrees.
Interior and Exterior Angles
To find the sum of the interior angle measures of a
convex polygon, draw all possible diagonals from
one vertex of the polygon.
Convex
Polygon
Number of
Sides
Number of
Triangles
Sum of the
interior
angles
In a regular polygon, the measure of EACH interior angle is:
Sum of the angles
Number of angles
1. Find the sum of the interior angle measures of a convex heptagon.
2. Find the sum of the interior angle measures of a convex 15-gon.
3. Find the measure of each interior angle of a regular 16-gon.
4. Find the measure of each interior angle of a regular decagon.
5. Find the measure of each interior angle of pentagon ABCDE.
Find x and y
“y” is called an Exterior Angle.
An exterior angle plus it’s adjacent interior angle adds up to 180 degrees.
All exterior angles in a any polygon adds up to 360 degrees.
Find the measure of an interior and
exterior angle for each regular
polygon.
 1) 72-gon
2) 18-gon
 3) 30-gon
4) octagon
 5) pentagon
6) dodecagon
The measure of an exterior angle is
given. Name the regular polygon it
belongs to.
1) 120 ̊
2) 60 ̊
3) 7.2 ̊
4) 14.4 ̊
5) 18 ̊
6) 72 ̊
Find the name of the polygon with:
 1) interior angles
that sum to 180 ̊.
 2) exterior angles that are 45 ̊ each.
 3) interior angles that are each 108 ̊.
 4) interior angles that are each 150
̊.
If each exterior angles of a regular
polygon measures 36 ̊, find the
sum of the measures of the interior
angles.
If each exterior angles of a regular
polygon measures 60 ̊, find the
sum of the measures of the interior
angles.
Find m∠E, if m∠ A = 160 ̊ ,
m ∠ B = 50 ̊ , m ∠ C and m ∠ D =
140 ̊ each.
Find m∠1 if m∠G = 80 ̊ ,
m∠F = 110 ̊ , m∠H = 74 ̊
The sum of the measures of five
interior angles of a hexagon is 525
degrees.
Find the measure of the 6th
angle.
 1)
2) Would this be a regular
hexagon?
Find the sum of three angles in
a regular decagon.
The measure of an exterior angle of
a regular octagon is (x+7). Find x
and the measure of each angle in
the octagon.
The sum of the measures of 8
interior angles of a nonagon is 1,110
degrees. Find the measure of the
9th angle.
Find the value of x.
Find the value of y
Find the value of b in polygon FGHJKL.
Ann is making paper stars for party decorations.
What is the measure of 1?
Lesson Quiz
1. Name the polygon by the number
of its sides. Then tell whether the
polygon is regular or irregular,
concave or convex.
nonagon; irregular; concave
2. Find the sum of the interior angle
measures of a convex 11-gon.
1620°
3. Find the measure of each interior angle of a
regular 18-gon. 160°
4. Find the measure of each exterior angle of a
regular 15-gon. 24°