Download IM2 Notes 8.1

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8.1 Notes: Polygon Interior Angles Sum
Lesson Objective: Find and use the sum of the
measures of the interior angles of a polygon.
CCSS: G.MG.1
You will need: colored pens, CR
This is Jeopardy!!!: This is the sum of the angles of a
triangle.
Lesson 1: Anatomy of a Polygon
Polygon: A closed plane figure formed by 3 or
more straight segments that intersect only at
their endpoints.
Lesson 1: Anatomy of a Polygon
Types of Polygons: Know these on p. 476!
Lesson 1: Anatomy of a Polygon
Regular: All sides and all angles are congruent.
Irregular: A polygon that is not regular.
Concave: When a diagonal contains points outside of
the polygon.
Convex: When no diagonals contain points outside of
the polygon.
Lesson 1: Anatomy of a Polygon
Plot a point P. Construct regular hexagon
ABCDEF inscribed in a circle with diameter 3”.
Lesson 1: Anatomy of a Polygon
Label as follows.
Regular Hexagon
Interior
Angle
Vertex
Side
Diagonal
Exterior Angle
Lesson 1: Anatomy of a Polygon
Measure an interior angle. _____ What
would the sum of the interior angles be? ____
Regular Hexagon
Interior
Angle
Vertex
Side
Diagonal
Exterior Angle
Lesson 2: Polygon Interior Angles Sum
Use a ruler to draw the following:
Triangle
Quadrilateral
Pentagon
Lesson 2: Polygon Interior Angles Sum
Starting at one vertex, draw diagonals to each
of the remaining vertices.
Triangle
Quadrilateral
Pentagon
Lesson 2: Polygon Interior Angles Sum
What is the sum of the interior angles in each
figure? Can you come up a formula?
Triangle
Quadrilateral
Pentagon
Lesson 2: Polygon Interior Angles Sum
The sum of the interior angle measures of
an n-sided convex polygon is (n – 2)180.
Triangle
Quadrilateral
Pentagon
Lesson 2: Polygon Interior Angles Sum
Example:
The number of sides = ____
The sum of the interior angles is:
( __ – 2)180 =
Lesson 3: Finding the Interior Angle Measures
and Sums in Polygons
A. Find the sum of the interior angle
measures of a regular convex heptagon.
B. Find the measure of each interior angle
of a regular convex heptagon.
Lesson 4: Using Algebra to Find the Interior
Angle Measures and Sums in Polygons
Find the measure of each interior angle of
pentagon ABCDE.
Lesson 5: Polygon Exterior Angles Sum
Construct an equilateral triangle using
your compass.
Lesson 5: Polygon Exterior Angles Sum
Lesson 5: Polygon Exterior Angles Sum
Sketch the following trapezoid. Label as
shown.
100° 120°
80°
60°
Lesson 5: Polygon Exterior Angles Sum
What is the measure of the exterior angles
of each polygon? Find the sum of the
exterior angles of each polygon.
100° 120°
80°
60°
Lesson 5: Polygon Exterior Angles Sum
What is the measure of an exterior angle
of a regular hexagon? ____ What would
the sum of the exterior angles be?
____________
Exterior Angle
Lesson 5: Polygon Exterior Angles Sum
What is the “formula” for the sum of
exterior angles of a polygon?
100° 120°
80°
60°
Lesson 5: Polygon Exterior Angles Sum
Polygon Exterior Angle Sum Theorem: The
sum of the exterior angle measures, one angle
at each vertex, of a convex polygon is 360°.
100° 120°
80°
60°
Lesson 6: Finding Exterior Angle Measures
A. Find the measure of each exterior angle
of a regular 20-gon.
B. Find the value of b in polygon FGHJKL.
Then find the
exterior angle
measures.
Lesson 7: Finding the Number of Sides
A. The measure of an exterior angle of a regular
polygon is 24°. Find the number of sides in
the polygon.
B. The measure of an interior angle of a regular
polygon is 144°. Find the number of sides in
the polygon.
8.1: Do I Get It? Yes or No
1. Name the polygon by the number of sides.
Tell whether it is regular or irregular and
whether it is concave or convex.
2. Find the sum of the interior angle measure of a
convex 11-gon.
3. Find the measure of each interior angle
measure of a regular 11-gon.
8.1: Continued
4. The measure of an exterior angle of a regular
polygon is 14.4°. Find the number of sides in
the polygon.
5. The measure of an interior angle of a regular
polygon is 135°. Find the number of sides in
the polygon.
6. Find the value
of x.
7. Find the sum
of the interior
angles for the
figure to the right.