2. Date: 8.1 Notes: Polygon Interior Angles Sum Lesson Objective: Find and use the sum of the measures of the interior angles of a polygon. CCSS: G.MG.1 You will need: colored pens, CR This is Jeopardy!!!: This is the sum of the angles of a triangle.

3. Lesson 1: Anatomy of a Polygon Polygon: A closed plane figure formed by 3 or more straight segments that intersect only at their endpoints.

4. Lesson 1: Anatomy of a Polygon Types of Polygons: Know these on p. 476!

5. Lesson 1: Anatomy of a Polygon Regular: All sides and all angles are congruent. Irregular: A polygon that is not regular. Concave: When a diagonal contains points outside of the polygon. Convex: When no diagonals contain points outside of the polygon.

6. Lesson 1: Anatomy of a Polygon Plot a point P. Construct regular hexagon ABCDEF inscribed in a circle with diameter 3”.

7. Lesson 1: Anatomy of a Polygon Label as follows. Regular Hexagon Interior Vertex Angle Side Diagonal Exterior Angle

8. Lesson 1: Anatomy of a Polygon Measure an interior angle. _____ What would the sum of the interior angles be? ____ Regular Hexagon Interior Vertex Angle Side Diagonal Exterior Angle

9. Lesson 2: Polygon Interior Angles Sum Use a ruler to draw the following: Triangle Quadrilateral Pentagon

10. Lesson 2: Polygon Interior Angles Sum Starting at one vertex, draw diagonals to each of the remaining vertices. Triangle Quadrilateral Pentagon

11. Lesson 2: Polygon Interior Angles Sum What is the sum of the interior angles in each figure? Can you come up a formula? Triangle Quadrilateral Pentagon

12. Lesson 2: Polygon Interior Angles Sum Triangle Quadrilateral Pentagon The sum of the interior angle measures of an n-sided convex polygon is (n – 2)180.

13. Lesson 2: Polygon Interior Angles Sum Example: The number of sides = ____ The sum of the interior angles is: ( __ – 2)180 =

14. Lesson 3: Finding the Interior Angle Measures and Sums in Polygons A.Find the sum of the interior angle measures of a regular convex heptagon. B.Find the measure of each interior angle of a regular convex heptagon.

15. Lesson 4: Using Algebra to Find the Interior Angle Measures and Sums in Polygons Find the measure of each interior angle of pentagon ABCDE.

16. Lesson 5: Polygon Exterior Angles Sum Construct an equilateral triangle using your compass.

17. Lesson 5: Polygon Exterior Angles Sum

18. Lesson 5: Polygon Exterior Angles Sum Sketch the following trapezoid. Label as shown. 100° 120° 80° 60°

19. Lesson 5: Polygon Exterior Angles Sum What is the measure of the exterior angles of each polygon? Find the sum of the exterior angles of each polygon. 100° 120° 80° 60°

20. Lesson 5: Polygon Exterior Angles Sum What is the measure of an exterior angle of a regular hexagon? ____ What would the sum of the exterior angles be? ____________ Exterior Angle

21. Lesson 5: Polygon Exterior Angles Sum What is the “formula” for the sum of exterior angles of a polygon? 100° 120° 80° 60°

22. Lesson 5: Polygon Exterior Angles Sum 100° 120° 80° 60° Polygon Exterior Angle Sum Theorem: The sum of the exterior angle mea­sures, one angle at each vertex, of a convex polygon is 360°.

23. Lesson 6: Finding Exterior Angle Measures A.Find the measure of each exterior angle of a regular 20-gon. B.Find the value of b in polygon FGHJKL. Then find the exterior angle measures.

24. Lesson 7: Finding the Number of Sides A.The measure of an exterior angle of a regular polygon is 24°. Find the number of sides in the polygon. B.The measure of an interior angle of a regular polygon is 144°. Find the number of sides in the polygon.

25. 8.1: Do I Get It? Yes or No 1.Name the polygon by the number of sides. Tell whether it is regular or irregular and whether it is concave or convex. 2.Find the sum of the interior angle measure of a convex 11-gon. 3.Find the measure of each interior angle measure of a regular 11-gon.

26. 8.1: Continued 4.The measure of an exterior angle of a regular polygon is 14.4°. Find the number of sides in the polygon. 5.The measure of an interior angle of a regular polygon is 135°. Find the number of sides in the polygon. 6. Find the value of x. 7. Find the sum of the interior angles for the figure to the right.