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GEOMETRY NOTES
LESSON 49: Angle Measures in Polygons
EXPLORATION: Investigating the Sum of Polygon Angle Measures
In each convex polygon, draw all the diagonals from one vertex. Notice that this divides each polygon into
triangular regions.
Complete the table below. What is the pattern in the sum of the measures of the interior angles of any convex
n-gon?
POLYGON
NUMBER OF SIDES
(n)
3
Triangle
Quadrilateral
Pentagon
Hexagon
.
.
.
n-gon
n
EXAMPLES: Find the sum of the interior angles of the polygon.
1. 13-gon
2. Dodecagon
YOU TRY:
3. 11-gon
NUMBER OF
TRIANGLES
SUM OF MEASURES OF
INTERIOR ANGLES
GEOMETRY NOTES
LESSON 49: Angle Measures in Polygons
EXAMPLES: Find the value of x.
4.
5.
YOU TRY:
6.
7.
GEOMETRY NOTES
LESSON 49: Angle Measures in Polygons
MEASURE OF EACH INTERIOR ANGLE IN A REGULAR POLYGON:
____________________________
EXAMPLES: Find the number of sides of the polygon.
8. The measure of each interior angle of a regular polygon is 140°. How many sides does the polygon have?
YOU TRY:
9. The measure of each interior angle of a regular polygon is 165°. How many sides does the polygon have?
EXTERIOR ANGLES IN A POLYGON:
________________________________________
EXAMPLES: Find the measure of the exterior angle, x.
10.
11.
GEOMETRY NOTES
LESSON 49: Angle Measures in Polygons
YOU TRY:
12.
13.
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