Download What is the sum of the measures of the interior angles of a polygon?

Lesson Plan #37
Date: Wednesday November 20th, 2013
Class: Geometry
Topic: Exterior angle of a triangle
Aim: What is the sum of the measures of the interior angles of a polygon?
Objectives:
1) Students will be able find the sum of the measures of the interior angles of a triangle.
2) Students will be able to find the sum of the measures of the exterior angles of a triangle.
HW #37: Page 104 #’s 1-6, 8, 9, 10, 11
Do Now:
Procedure:
Write the Aim and Do Now
Get students working!
Take attendance
Give Back HW
Collect HW
Notice each of the interior angles of the polygons at right measures
less than 180o. These are known as convex polygons.
If the polygon has at least one angle measuring more than 180o, it is
called a concave polygon.
Question: What do we call a polygon whose sides are all the same length and whose angles are all the same measure?
Online Interactive Activity : Let’s see regular polygons in action. Let’s go to
http://www.mathopenref.com/polygonregular.html
So we stated that the sum of the angles of a triangle is 180 o and the sum of the angles of a quadrilateral
is 360o. Let’s see how we can find the sum of the angles of a pentagon, then try to generalize a formula
for the sum of the interior angles of a polygon of n sides. Examine the pentagon below. To help you
discover the formula, see how many non-overlapping triangles you can create, then use this to come up
with a sum of the angles of a pentagon.
Try it for a six sided figure (hexagon).
What is the formula for the sum of the interior angles of a polygon with n sides?
Online Interactive Activity : Let’s check out the sum of the interior angles of a polygon
in action. Let’s go to http://www.mathopenref.com/polygoninteriorangles.html
Online Interactive Activity Let’s check out the sum of the exterior angles of a polygon, taking one exterior angle at each
vertex.
http://www.mathopenref.com/polygonexteriorangles.html
What is the formula for the sum of the exterior angles of any polygon of n sides, taking one exterior angle at each vertex?
Sample Test Questions:
1)
2) What is the sum of the interior angles of a regular dodecagon (12-sided polygon)?
3) Each of the interior angles of a regular polygon is 156°. How many sides does the polygon
have?
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Assignment: Complete the exercises below