Learn How to Find the Measures of Angles in Triangles

1. SWBAT find the measures of angles of triangles using the Triangle Sum Theorem and Triangle Exterior Angle Theorem Agenda 1. Warm-up (10 min) 2. Review HW (20 min) 3. New notes / exit slip (5 15 min) Warm-Up: 1. What is 80% of 90% of 10? 2. What is 20% of 15% of 100? 3. What is 25% of 70% of 150? (round to nearest tenth) HW: Read Pgs 353-355 Do Pg. 356 #1-#3 Quiz Thursday! Mon, 2/3

2. The sum of the interior measures of the angles of a triangle is 180 degrees. Triangle Sum Theorem

3. The measures of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles. Triangle Exterior Angle Theorem

5. Review HW: Page 175: #1 #21 ALL Page 177: #29 #32 ALL

6. Exit Slip: sheet Collected 1.) Find the value of x , y , and z ? 3.) Find m<1 and m <2. 2.) Find the value of x

7. Summary Be VERY specific! 1. Sum of interior angles of a triangle = 180 0 2. Exterior angle = Sum of interior angles in triangle

8. SWBAT find the sum of the measures of interior and exterior angles of a polygon. Agenda 1. Warm-up / HW Check (10 min) 2. New notes / practice problems (40 min) Warm-Up: 1. What is 40% of 5/2? 2. What is 65% of ? 3. What is 80% of 7/12? Pg. 356 #1 #3, Pg. 356 #7 #25 ALL Quiz Thursday! Tues, 2/4

9. Chapter 6.1 Polygon Angle Sum

10. Polygon A closed plane figure formed by 3 or more segments that all lie in one plane

11. Polygons are named by number of sides Number of Sides Polygon 3 4 5 6 7 8 9 10 12 n Triangle Quadrilateral Pentagon Hexagon Heptagon Octagon Nonagon Decagon Dodecagon n-gon

12. An equilateral polygon: All sides congruent. An equiangular polygon : All angles congruent. A regular polygon : All the sides and angles congruent. Equilateral Polygon Equiangular Polygon Regular Polygon

13. Concave If any part of a diagonal contains points in the exterior of the polygon.

14. Convex If no diagonal contains points in the exterior. A regular polygon is always convex.

15. SWBAT find the sum of the measures of interior and exterior angles of a polygon. Agenda 1. Warm-up (10 min) 2. Notes / practice problems (40 min) Warm-Up: 1. Al is paid 35% as much as Franklin. If Franklin is paid $24.00 per hour, how much is Al paid per hour? 2. Nancy gets paid $12.00 per hour at her job at the grocery store. Susie is paid 120% as much as Nancy. How much is Susie paid per hour? Pg. 356 #1 #3, Pg. 356 #7 #25 ALL Quiz Tomorrow! Wed, 2/5

16. Polygon # of sides ( n ) # of triangles Sum of interior angles of a polygon Triangle Quadrilateral Pentagon Hexagon Heptagon Octagon n-gon 3 4 5 6 7 8 n 3 4 5 6 n 2 2 1 180 2 180 = 360 3 180 = 540 4 180 = 720 5 180 = 900 6 180 = 1080 ( n 2) 180

17. Ex: What is the measure of angle Y in pentagon TODAY?

18. SWBAT find the sum of the measures of interior and exterior angles of a polygon. Agenda 1. Warm-up (10 min) 2. Notes / practice problems (40 min) Warm-Up: 1. Tomas bought a new book on sale. It cost $17.95 but was on sale for 20% off. How much did the book cost Tomas? 2. Roman bought a shirt for $11.25. He was able to receive a discount on the shirt for 30% off. How much did Roman pay for the shirt? Pg. 421 #5 10 Fri, 2/6

19. Polygon Angle-Sum Theorem The sum of the measures of the interior angles of an n- gon is: Sum = ( n 2)180 n = the number of sides

20. Ex: What is the sum of the measures of the interior angles of an octagon? Sum = ( n 2)180 = (8 2)180 = 6 * 180 = 1,080

21. 1. Ex: If the sum of the measures of the interior angles of a convex polygon is 3600 , how many sides does the polygon have. (n 2)180 = 3600 180n 360 = 3600 + 360 + 360 180n = 3960 180 180 n = 22 sides (n 2)180 = Sum

22. 1. Ex: If the sum of the measures of the interior angles of a convex polygon is 2340 , how many sides does the polygon have. (n 2)180 = 2340 180n 360 = 2340 + 360 + 360 180n = 2,700 180 180 n = 15 sides (n 2)180 = Sum

23. 4x 2 82 108 2x + 10 108 + 82 + 4x 2 + 2x + 10 = (4 2)180 6x + 198 = 360 6x = 162 6 6 x = 27 Ex: Solve for x Sum = (n 2)180

24. Ex. Find the values of the variables and the measures of the angles. x = 25 130 0 90 0 115 0 115 0 90 0

25. The measure of each interior angle of a regular n -gon is

26. Ex: What is the measure of each or one interior angle in a regular octagon? (8 2)180 / 8 135 0

27. What do you notice about the exterior angles of the polygons below?

28. Polygon Exterior Angle-Sum Theorem The sum of the measures of the exterior angles of a polygon, one at each vertex, is 360.

29. Ex. Find the exterior angle sum of a decagon.

30. 54 68 65 (3x + 13) 60 (4x 12) Sum of exterior angles is 360 (4x 12) + 60+ (3x + 13) + 65 + 54+ 68 = 360 7x + 248 = 360 248 248 7x = 112 7 7 x = 12 Ex: Find the value of x

31. Ex: What is the measure of angle 1 in the regular octagon?