1. Unit 3 Comp 4 Interior/Exterior Angles of a Polygon
R.4.G.2 Solve problems using properties of polygons:
sum of the measures of the interior angles of a polygon
interior and exterior angle measure of a regular polygon or irregular polygon
number of sides or angles of a polygon

2. Definitions
Interior Angle: The inside angle of a polygon formed by two adjacent sides
Exterior Angle: The angle formed when one side of a polygon is extended (adjacent to an interior angle)
Remote Interior Angles: In a triangle, the two angles that are not adjacent to a specific exterior angle

3. Exterior Angles Lab Name the interior angles: _______ _______C D
Name the interior angles: _______
_______
Name the exterior angle shown:_______
Which interior angles are remote interior angles?

4. Part 1: Measure each angle with your protractor and record your results in the chart. . .B C D +

5. Part 1 (continued): X W Y Z +

6. Conjecture:
The measure of an exterior angle of a triangle is equal to:
The sum of the interior angles of a triangle is always:
The sum of the
remote interior angles!
180 degrees!

7. Examples
Find the value of the variable for each triangle. Classify each triangle by its angles.
120o y x
40o
60o x

8. You Try… 180-84-27 = x X = 69o 180-90-65 = z Z = 25o Y = 84 + 27

9. You Try… 2x+5 + x-25 + 2x = 180 5x – 20 = 180 5x = 200 X = 40
(2x + 5)o
(x - 25)o
2xo
2x+5 + x x = 180
5x – 20 = 180
5x = 200
X = 40
78 + y = 110
Y = 32o
78+32+x = 180
X = 70o

10. Polygons
Polygon: A geometric figure formed by line segments that meet at their endpoints, do not cross, and completely enclose part of a plane.

11. Draw Examples of . . . Polygons Not Polygons

12. Definitions
Convex Polygon: A polygon in which no segment connecting two vertices is outside the polygon
Examples:

13. Definitions
Concave Polygon: A polygon in which at least one segment connecting two vertices is outside the polygon.
Examples:

14. Definitions Consecutive Sides: Consecutive Vertices:
Consecutive Angles:
Two sides that share a common vertex
Two vertices connected by a side
Two angles that share a common side

15. Classifying Polygons According to Numbers of Sides
Number of Sides
Name of Polygon 1 2 3 4 5 6
Not a polygon
Not a polygon
Triangle
Quadrilateral
Pentagon
Hexagon

16. Classifying Polygons According to Numbers of Sides
Number of Sides
Name of Polygon 7 8 9 10 11 12 n
Heptagon
Octagon
Nonagon
Decagon
Hendecagon
Dodecagon
N-gon