1. 11.1: Angle Measures in Polygons
GEOMETRY: Chapter 11
11.1: Angle Measures in Polygons

2. Theorem 11.1: Polygon Interior Angles Theorem
The sum of the measures of the interior angles of a convex n-gon is (n – 2)(180o).
Image taken from: Geometry. McDougal Littell: Boston, P. 507.

3. Corollary to Theorem 11.1: Interior Angles of a Quadrilateral
The sum of the measures of the interior angles of a quadrilateral is 360o.

4. Ex.1:
Find the sum of the measures of the interior angles of a convex decagon.
Answer: 1440 degrees

5. Ex. 2:
The sum of the measures of the interior angles of a convex polygon is 2340o. Classify the polygon by the number of sides.
Answer: 15-gon

6. Find the value of x in the diagram shown.
Ex. 3:
Find the value of x in the diagram shown.
Answer: 154
Images taken from: Geometry. McDougal Littell: Boston, P.508.

7. Exterior Angles—Unlike the sum of the interior angle measures of a convex polygon, the sum of the exterior angle measures does NOT depend on the number of sides of a polygon.

8. Polygon Exterior Angles Theorem
The sum of the measures of the exterior angles of a convex polygon, one angle at each vertex, is 360o.
Image taken from: Geometry. McDougal Littell: Boston, P. 509.

9. What is the value of x in the diagram shown?
Ex. 4:
What is the value of x in the diagram shown?
Answer: 66
Image taken from: Geometry. McDougal Littell: Boston, P. 509.

10. Ex. 5:
A stop sign is shaped like a regular octagon. Find (a) the measure of each interior angle and (b) the measure of each exterior angle.
Answer: a) 135 degrees; b) 45 degrees

11. 11.1, p. 664, #3-25 all