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Understanding Interior and Exterior Angles of Polygons

In today's class, we will explore the concepts of interior and exterior angles in polygons. We'll begin with a warm-up exercise involving regular octagons and 11-gons. After reviewing homework on convex and concave polygons, we’ll dive into calculations for angle measurements based on polygon properties. Key topics include the sum of interior angles, the relationship between interior and exterior angles, and the implications for various types of polygons. Homework will focus on finding angles and applying geometric principles.

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Understanding Interior and Exterior Angles of Polygons

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  1. Math 1 March 19th What you need today in class: • Pick up a calculator and warm-up sheet • Turn in Homework – page 18 WARM-UP (Don’t copy question – just show work and give answer) Find the measure of ONE exterior angle of a regular octagon. Find the measure of ONE interior angle of a 11-gon.

  2. CHECK HOMEWORK – FRONT 1. CONVEX POLYGON 2. CONCAVE POLYGON 3. NOT A POLYGON 4. QUADRILATERAL PENTAGON HEXAGON OCTAGON DECAGON N-GON 5. 180(n – 2) 6. 360O 7. 360°/360° 8. 720o/360o 9. 1440°/360° 10. 540o/360o 11. 1080°/360° 12. 2880o/360o 15. REGULAR 16. 60o/120o 17. 120°/60° 18. 144o/36o

  3. Summary Notes on Page 12 Interior Angle SUM ONE Interior Angle Exterior Angle SUM ONE Exterior Angle

  4. Ex. 4 Each exterior angle of a polygon is 18. How many sides does it have? n = 20

  5. Ex. 5 The sum of the measures of five interior angles of a hexagon is 535. What is the measure of the sixth angle? 185°

  6. Ex. 6 The measure of the exterior angle of a quadrilateral are x, 3x, 5x, and 3x. Find the measure of each angle. 30°, 90°, 150°, and 90°

  7. Ex. 7 If each interior angle of a regular polygon is 150, then how many sides does the polygon have? n = 12

  8. Notes: p. 16 • INTERIOR ANGLES 1. How do you find the sum of ALL of the INTERIOR ANGLES of a polygon?

  9. INTERIOR ANGLES 1. How do you find the sum of ALL of the INTERIOR ANGLES of a polygon? 2. How do you find the measure of ONE INTERIOR ANGLE of a REGULAR polygon?

  10. INTERIOR ANGLES 1. How do you find the sum of ALL of the INTERIOR ANGLES of a polygon? 2. How do you find the measure of ONE INTERIOR ANGLE of a REGULAR polygon? 3. How do you find the measure of ONE INTERIOR ANGLE of a non-regular polygon?

  11. EXTERIOR ANGLES 1. The sum of the measures of ALL the EXTERIOR ANGLES of a polygon is always ______.

  12. EXTERIOR ANGLES 1. The sum of the measures of ALL the EXTERIOR ANGLES of a polygon is always ______. 2. How do you find the measure of ONE EXTERIOR ANGLE of a REGULAR polygon?

  13. FINDING AN INTERIOR & EXTERIOR ANGLE AT THE SAME TIME An interior angle and an exterior angle form a __________ ____________.

  14. FINDING AN INTERIOR & EXTERIOR ANGLE AT THE SAME TIME An interior angle and an exterior angle form a __________ ____________. 1st: Find the EXTERIOR ANGLE 2nd: Find the INTERIOR ANGLE using the linear pair relationship. a) Find the interior and exterior angle of a regular hexagon.

  15. HOMEWORK • PAGE 19

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