Bell Work
1.
Find x
2. Find x and y
Polygons
Day 1 – Interior Angles
This is a chart
Polygon
Triangle
# of Sides
# of Triangles
3
1
Quadrilateral
4
2
Pentagon
5
3
Hexagon
6
4
Heptagon
7
5
Octagon
8
6
N-gon
n
n -2
Sum of the
Angle
Measures
Interior Angle
Measures
Example 1
• Ryan’s parents are building him a sandbox to play in. It is the
shape of a hexagon as shown. What is the sum of the
measures of the interior angles of the hexagon?
𝑆 = 180(𝑛 − 2)
𝑆 = 180(6 − 2)
𝑆 = 180 4 = 720
Example 2
• The sum of the angles inside a polygon is 2340 degrees. Find
the number of sides on this polygon.
Example 3
• Find the value of x.
Example 4
• Find the value of x.
Regular (Defn)
• Definition:
• Can you name a regular quadrilateral?
• A regular triangle?
How do we find interior angles?
Polygon
Triangle
# of Sides
# of Triangles
Sum of the
Angle
Measures
3
1
180
Quadrilateral
4
2
360
Pentagon
5
3
540
Hexagon
6
4
720
Heptagon
7
5
900
Octagon
8
6
1080
N-gon
n
n-2
180(n-2)
Interior Angle
Measures
Example 5
• A regular polygon with each interior angle is 140 degrees. How
many sides does the polygon have?
HOMEWORK
• 6.1 Pg 320 #’s 1-3, 7-9, 13-15, 19-20
Bell Work
• A mall is designed so that 5
walkways meet at a food
court that is in the shape of
a regular pentagon. Find the
sum of the measures of the
interior angles of the
pentagon.
• A polygon that has 53 sides
has how many degrees in all
of their interior angles?
Polygons
Day 2 – Exterior Angles
Sum of Exterior Angles
• An exterior angle is formed when one side at a vertex of a
polygon is extended.
• The sum of ALL the exterior angles is 360°. FOR EVERY
POLYGON!!!
• This is because the angles rotate around to make one
revolution. (circle-has 360 degrees)
Example 1
• Find the sum of the exterior angles and the measure of each
exterior angle of a…
1. quadrilateral
2. 100-gon
3. nonagon
Example 2
• A hexagon has an exterior angle that measures…
• The formula for each exterior angle is:
360
𝐸=
𝑛
Example 3
• A polygon has an exterior angle of 18 degrees. How many
sides does the polygon have?
Example 4
• Find the interior and exterior angle measure of a dodecagon
Challenge
• The ratio for an exterior angle to an interior angle is 1:3. How
many sides are in the shape.
Homework
• 6.1 Pg 321 #’s 10, 16, 17, 23-26, 31