Download Geometry. - cloudfront.net

GEOMETRY: Chapter 11
11.1: Angle Measures in Polygons
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, 2007. P. 507.
Corollary to Theorem 11.1: Interior
Angles of a Quadrilateral
The sum of the measures of the interior
angles of a quadrilateral is 360o.
Ex.1:
Find the sum of the measures of the interior
angles of a convex decagon.
Answer: 1440 degrees
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
Ex. 3:
Find the value of x in the diagram shown.
Answer: 154
Images taken from: Geometry. McDougal Littell: Boston, 2007. P.508.
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.
Theorem 11.2:
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, 2007. P. 509.
Ex. 4:
What is the value of x in the diagram shown?
Answer: 66
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 509.
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
11.1, p. 664, #3-25 all