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Polygon Exterior Angle Sum Theorem

Polygon Exterior Angle Sum Theorem. During this lesson, you will solve statement problems involving Polygon Exterior Angle Sum Theorem and its corollary. Vocabulary. If you extend one side of a polygon from one endpoint, then you have constructed an ____________at the vertex. I n t e

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Polygon Exterior Angle Sum Theorem

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

  2. Vocabulary If you extend one side of a polygon from one endpoint, then you have constructed an ____________at the vertex. I n t e r i o r exterior angle Exterior angle Geometry

  3. Alert! Each student has been given a different pair of polygons. 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. Geometry

  4. The sum of the measures of one set of exterior angles of a convex polygon is 360°. 1 3 2 Geometry

  5. The sum of the measures of one set of exterior angles of a convex polygon is 360°. 1 2 4 3 Geometry

  6. 2 1 3 5 4 The sum of the measures of one set of exterior angles of a convex polygon is 360°. Geometry

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

  8. Polygon Exterior Angle Sum Theorem Use this information to complete the final column of your polygon sum chart! 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 ____________. 360 360 n Geometry

  9. Solving Statement Problems Using Polygon Exterior Angle Sum Theorem 360 360 n 360 = n KEY: Translate Words  Symbols Geometry

  10. 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? Geometry

  11. Assume that all polygons are regular to complete the chart below: R E A D Geometry

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

  13. Final Check: Now, try these problems which follow without any help! Geometry

  14. Find the measure of ONE exterior angle of a regular 20-gon. 18° Geometry

  15. The sum of the measures of five interiorangles of a hexagon is 625. What is the measure of the sixth angle? 95° Geometry

  16. Homework Assignment Polygon Exterior Angle Supplemental WS, plus textbook: _____________ Geometry

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