Download 3.4: The Polygon Angle

3.4: THE POLYGON
ANGLE-SUM THEOREM
OBJECTIVE: STUDENTS WILL BE ABLE TO…
•
TO CLASSIFY POLYGONS, AND TO FIND THE SUMS OF
INTERIOR AND EXTERIOR ANGLES OF POLYGONS
HELLO!!! It’s going to be a
good day 
POLYGON:
• CLOSED PLANE FIGURE
• AT LEAST 3 SIDES THAT ARE SEGMENTS
• SIDES INTERSECT ONLY AT ENDPOINTS
• ADJACENT SIDES ARE NOT COLLINEAR
POLYGONS
NOT POLYGONS
TO NAME A POLYGON:
• START AT ANY VERTEX
• LIST VERTICES CONSECUTIVELY
NAME THE POLYGON. NAME THE SIDES AND ANGLES.
B
A
C
E
D
COMMON POLYGONS:
SIDES
NAME
3
Triangle
4
Quadrilateral
5
Pentagon
6
Hexagon
8
Octagon
9
Nonagon
10
Decagon
12
Dodecagon
n
n- gon
DIAGONAL OF A POLYGON
• A SEGMENT IN A POLYGON DRAWN FROM A VERTEX TO A
NONADJACENT VERTEX
CONVEX VS. CONCAVE
CONVEX POLYGON
CONCAVE POLYGON
• NO DIAGONAL WITH POINTS
OUTSIDE POLYGON
• AT LEAST ONE DIAGONAL
OUTSIDE POLYGON
POLYGON-ANGLE-SUM THEOREM
THE SUM OF THE MEASURES OF ANGLES IN AN N-GON :
(N-2)180
EXAMPLE:
FIND THE SUM OF THE MEASURES OF A 15-GON.
FINDING MISSING ANGLE MEASURES
• FIGURE OUT WHAT THE SUM OF THE INTERIOR ANGLES SHOULD BE
• ADD UP EXPRESSIONS AND SET THEM EQUAL TO THE SUM FROM
PART ONE.
EXAMPLE: FIND Y.
y°
120°
85°
53°
Example:
1. The sum of the measures of a given polygon is
720. How many sides are in the polygon?
2.Pentagon ABCDE has 5 congruent angles. Find
the measure of each angle.
POLYGON-EXTERIOR-ANGLE SUM
THEOREM
THE SUM OF THE MEASURES OF EXTERIOR ANGLES OF A POLYGON IS
ALWAYS 360⁰.
EXAMPLE:
WHAT IS THE SUM OF EXTERIOR ANGLES FOR A
500-GON?
EQUILATERAL POLYGON: All sides

EQUIANGULAR POLYGON: All angles

REGULAR POLYGON: equilateral and
equiangular
If you have a REGULAR POLYGON, to find:
ONE Interior

Measure:
(n  2)180
n
ONE Exterior
 measure:
360
n
Examples:
1. The sum of the measures of angles of a polygon
with n sides is 1980. Find n, the number of sides.
2. Find the measures of one interior angle and one
exterior angle of a REGULAR hexagon.
3. The measure of an exterior angle of a regular
polygon is 30⁰. What is the measure of an interior
angle? How many sides are there?
TYPE 2: WRITE AND ANSWER THE FOLLOWING ON A
SEPARATE PIECE OF PAPER. (2 POINTS EACH QUESTION)
1.
FIND THE SUM OF THE INTERIOR AND EXTERIOR ANGLES OF
AN OCTAGON.
2.
FIND THE MEASURE OF ONE INTERIOR ANGLE AND ONE
EXTERIOR ANGLE OF A REGULAR 15-GON.
3.
THE SUM OF THE INTERIOR ANGLES OF A POLYGON IS
4680°. FIND THE NUMBER OF SIDES.