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Section 6.1- The Polygon Angle-Sum Theorems
Essential Question: How are triangles and polygons related?
Do Now:
How can you find the measures of the angles of the polygons based on the number of
triangles formed?
Special Polygons
Example 1: Applying Polygon-Angle Sum Theorem
a. What is the sum of the interior angle measures of a 17-gon?
b. If you have a regular 17-gon, what is the measure of each angle?
c. The sum of the interior angle measures of a polygon is 1980. How can you find the
number of sides in the polygon?
Example 2: Using the Polygon Angle-Sum Theorem
What is 𝑚∠𝐺 in quadrilateral EFGH?
Discovering the Exterior-Angle Sum Theorem
Find the SUM of the exterior angles in each polygon. What do you notice?
Example 3: Finding an Exterior Angle Measure
What is the measure of an exterior angle of a regular nonagon?
Group Work
1. A triangle has two congruent interior angles and an exterior angle that measures 100.
Find two possible sets of interior angle measures for the triangle. Sketch each triangle
with the appropriate angle measures.
2. Find the value of each variable.
HW: p. 356-357 #7-13 odds, 15-19, 22-25, 29, 31, 32-36 evens
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