Angle Measures of Polygons Chapter 8 Section 1 Angle Measures of Polygons

Polygon Interior Angles Theorem The sum of the measures of the interior angles of a convex n-gon is:

Polygon Interior Angles Theorem The sum of the measures of the interior angles of a convex n-gon is:

Applying the Polygon Interior Angles Theorem Sum of interior angles Angle Measures if regular Triangle (3-gon) 180o 60o Quadrilateral 360o   90o Pentagon 540o 108o Hexagon 720o 120o Octagon 1080o 135o Decagon 1440o 144o Dodecagon 1800o 150o 15-gon 2340o 156o

Example 1: What is the sum of the interior angles of a convex nonagon?

Example 2: We are told that a convex n-gon has an interior angle sum of 1620°. How many sides does the polygon have?

Example 3: Find the measure of angle X from the polygon to the right.

What if we forget the formula?

Example 4: Use triangles to determine the sum of the interior angles of this polygon.

Try these! 2. Find the measure of angle X below. 1. What is the interior angle sum of a convex 22-gon?

Exterior Angles of a Convex Polygon The sum of the exterior angles, one at each vertex, of a convex polygon is:

Exterior Angles of a Convex Polygon The sum of the exterior angles, one at each vertex, of a convex polygon is:

Example 4: Solve for x in the following diagram:

Workbook Page 145-146 #16-21, 22-34even Homework Workbook Page 145-146 #16-21, 22-34even