Download 4-6-int-ext-angles

Name:
Geometry Period
4-6 Notes
Date:
Learning Goals: How do you find the measure of the sum of interior and exterior angles in a polygon? How do you find
the measures of the angles in a regular polygon?
Warm-Up
1. What is similar about these two polygons?
What is different about these two polygons?
2. Given that a regular hexagon has an interior angle measure of 120 degrees. What will be the sum of all of the
interior angles of a regular hexagon?
3. Why is it important that we specify that the hexagon is regular?
What is a regular polygon?
Discovering the Rule for Finding the Total Degrees in Polygons
What is the total number
degrees of the interior angles of
triangle on the right?
Number of Sides
Number of
Triangles
Total Degrees
Divide the polygon into the fewest triangles possible and then figure out the total number of degrees in the polygon.
Shape
Number of
Sides
Number of
Triangles
Total Degrees
Picture
What Conclusions Can You Make?
Sum of the Interior Angles in a Polygon (does not need to be a regular polygon)
In Words:
As a Formula:
How can we figure out how much each interior angle is in a regular polygon?
Consider the regular pentagon to the right:
(a) What is the least number of degrees the pentagon can be rotated to that it is mapped back onto itself?
Flashback!
How do we
calculate this?
(b) What do we call the angle that is marked for us? _______________________
Therefore, the exterior angle of a regular polygon is ______________ to the least number of degrees it
needs to be rotated to map back onto itself.
We calculate this by:
(c) How can we use the exterior angle to find the measure of one interior angle? Try it!
Interior angles
and exterior
angles are
_____________.
Continuing Connections!
(d) Find the sum of all the exterior angles in the pentagon: ___________
The sum of the interior angles of a
polygon is always __________.
What conclusions can we make from today?

To calculate the sum of the interior angles of a regular polygon, use the formula _____________________.

The sum of the exterior angles of a polygon is always _________________.

To calculate one exterior angle (of a regular polygon) always use___________________________.

To calculate one interior angle (of a regular polygon) always use 180 – (the exterior angle measure)
because interior angle exterior angles are ________________________.
Let’s Apply It!
1)
a) Find the sum of the degree of the measures of the interior angles of a
regular polygon that has 8 sides.
b) Find the measure of one interior angle.
2) Find the number of sides in a polygon whose sum of the interior angles is 1440.
*Wait, How is this question different from example 1?
3) Show your work to calculate the number of degrees in each interior angle of a regular heptagon?
(Round to the nearest tenth)
4)
a. Determine the measure of degrees of each exterior angle in a regular octagon.
b. Find the sum of these angles.
5) The measure of 7 interior angles of an octagon are 91,175,150,156,90,175,178.
a) What is the measure of the 8th angle? What property/fact/concept did you use
to help you get this answer?
b) Is this angle acute or obtuse?
c) Is this octagon regular? Why or Why not?
6) We are looking for the measure of angle x. What is the measure of angle x?
Need Help
Getting Started
With Number 1?
*Since they tell us
we are dealing
with interior
angles of an
octagon, start by
finding the total
sum of the angles
using our formula.
*Now, we are
already given 7
angles...what can
we do to find the
last one?
7) Given the diagram below, find the missing angles listed. Also, state how you arrived at your answer for
each. (For example, if you knew 2 angles were a linear pair, you would say that…)
Angle Measure
How We Got Our Answer
m<1 = ______________________
______________________________
m<2 = _____________________
______________________________
m<3 = ______________________
______________________________
m<4 = ______________________
_______________________________
m<5 = _______________________
_______________________________
m<6 = _______________________
_______________________________
8) If each exterior angle of a regular polygon is 72 degrees, what type of polygon do we have?
9) Is it possible for an interior and an exterior angle to both be obtuse? Explain.