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Geometry sirimanne 0910 Unit 6 // Lesson 2 // Properties of Polygons Name: Date: Period: 1 2 3 4 5 6 Holt: 6‐1 Properties of Polygons p. 382 Standards: 12.0 Objective Interior Angles of Convex Polygons Polygon Angle Sum Theorem Polygon
A picture of a polygon, not necessarily
regular
n-sided polygon
Name of polygon # of sides
Number of triangles
After drawing diagonals
from one vertex, how
many triangles?
Sum of measures
of interior angles
# of triangles times
180º
Measure of
Interior angle if
regular
Polygon Interior Angle Sum Theorem 6‐1‐2 Polygon Angle Sum Theorem The sum of the measures of the interior angles of a convex n‐gon is:
Practice 1. What is the sum of the interior angles of a convex nonagon? 2. What is the measure of the interior angle of a regular octagon? 3. What is the sum of the interior angles of a convex 15‐gon? 4. What is the measure of the interior angle of a regular hexagon? 5. What is the sum of the interior angles of a convex 20‐gon? 6. What is the measure of the interior angle of a regular 20‐gon? Polygon Exterior Angle Sum Theorem 6‐1‐2 Polygon Angle Sum Theorem The sum of the measures of the exterior angles of a convex n‐gon is:
Polygon # of sides 3 4 5 6 7 8 9 10 n‐gon Practice 1. What is the sum of the exterior angles of a convex 13‐gon? 2. What is the measure of the exterior angle of a regular 12‐gon? Holt Bookwork p.386 [16‐26, 29‐34 ] Sum of exterior angles Exterior angle measures of regular polygon