Lesson 6­1 Angles of Polygons with answers.notebook
January 07, 2015
Questions/Main Ideas Lesson 6­1 Angles of Polygons
diagonal ­ a segment that connects any two nonconsecutive vertices
Theorem 6.1
Polygon Interior Angles Sum
The sum of the interior measures of an n­sided convex polygon is (n ­ 2) 180.
Ex: n = 6
S = 180(n ­ 2)
= 180(6 ­ 2)
= 720
Questions/Main Ideas
Example 1
a. Find the sum of the measures of the interior angles of a convex nonagon.
b. Find the measure of each interior angle of parallelogram RSTU.
1
Lesson 6­1 Angles of Polygons with answers.notebook
January 07, 2015
Questions/Main Ideas Example 2
A mall is designed so that five walkways meet at a food court that is in the shape of a regular pentagon. Find the measure of one of the interior angles of the pentagon.
Example 3
The measure of an interior angle of a regular polygon is 150. Find the number of sides in the polygon.
Questions/Main Ideas Theorem 6.2
Polygon Exterior Angles Sum The sum of the exterior angle measures of a convex polygon, one angle at each vertex, is 360.
Ex:
2
Lesson 6­1 Angles of Polygons with answers.notebook
January 07, 2015
Questions/Main Ideas Example 4
Find the measures of an exterior angle and an interior angle of convex regular nonagon ABCDEFGHJ.
Questions/Main Ideas Example 5
a. Find the value of x in the diagram.
b. Find the measure of each exterior angle of a regular decagon.
3
Lesson 6­1 Angles of Polygons with answers.notebook
January 07, 2015
4