Mrs. McConaughyGeometry1 Polygon Exterior Angle Sum Theorem During this lesson, you will solve statement problems involving Polygon Exterior Angle Sum.

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Objectives Classify polygons based on their sides and angles.

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Presentation transcript:

Mrs. McConaughyGeometry1 Polygon Exterior Angle Sum Theorem During this lesson, you will solve statement problems involving Polygon Exterior Angle Sum Theorem and its corollary.

Mrs. McConaughyGeometry2 Vocabulary If you extend one side of a polygon from one endpoint, then you have constructed an ____________at the vertex. exterior angle Exterior angle InteriorInterior

Mrs. McConaughyGeometry3 Investigation: Polygon Exterior Angle Sum Theorem Alert! All polygons have two sets of exterior angles. Draw one set of exterior angles. Measure each angle, then determine the sum of the entire set. Complete the theorem which follows. Alert! Each student has been given a different pair of polygons.

Mrs. McConaughyGeometry The sum of the measures of one set of exterior angles of a convex polygon is 360°.

Mrs. McConaughyGeometry The sum of the measures of one set of exterior angles of a convex polygon is 360°.

Mrs. McConaughyGeometry6 The sum of the measures of one set of exterior angles of a convex polygon is 360°

Mrs. McConaughyGeometry7 The measure of each exterior angle of a regular (equiangular, or equilateral) polygon is one

Mrs. McConaughyGeometry8 Polygon Exterior Angle Sum Theorem Polygon Exterior Angle Sum Theorem: The sum of the measures of the exterior angles of any n-gon is ________. Corollary: The measure of one exterior angle of any regular n-gon is ____________. 360 n Use this information to complete the final column of your polygon sum chart!

Mrs. McConaughyGeometry9 Solving Statement Problems Using Polygon Exterior Angle Sum Theorem KEY: Translate Words  Symbols Algebraic Expressions (Chart) Algebraic Equations “How many sides…?” Sum of Measure of exterior each angle angles if regular How many sides does a regular polygon have if each exterior angle measures _____? 360 n 360 = n

Mrs. McConaughyGeometry10 Sample Problems  a. What is the sum of the measures of the exterior angles of a decagon?  b. What is the measure of each exterior angle of a regular decagon?  c. (How many sides) does a regular polygon have if the measure of one exterior angle is 36?

Mrs. McConaughyGeometry11 Assume that all polygons are regular to complete the chart below: NUMBER OF SIDES6 SUM OF INTERIOR ANGLES 156 MEASURE OF EACH EXTERIOR ANGLE 90 MEASURE OF EACH INTERIOR ANGLE 135 READREAD

Special Case: Exterior Angle in a Triangle Mrs. McConaughyGeometry12 A a b c x B C D Remote interior angles Exterior angle EXTERIOR ANGLE CONJECTURE: The measure of an exterior angle of a triangle equals the sum of the two remote interior angles. m x = m a + m b

Mrs. McConaughyGeometry13 Final Check: Now, try these problems which follow without any help!

Mrs. McConaughyGeometry14 Find the measure of ONE exterior angle of a regular 20-gon. 18°

Mrs. McConaughyGeometry15 The sum of the measures of five interior angles of a hexagon is 625. What is the measure of the sixth angle? 95°

Mrs. McConaughyGeometry16 Homework Assignment Polygon Exterior Angle Supplemental WS, plus textbook: _____________