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

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

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

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

6. Exit Slip: ½ 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! Sum of interior angles of a triangle = 1800
Exterior angle = Sum of interior angles in triangle

8. What is 40% of 5/2? What is 65% of ¾? What is 80% of 7/12? Warm-Up:
Tues, 2/4
SWBAT… find the sum of the measures of interior and exterior angles of a polygon.
Agenda
Warm-up / HW Check (10 min)
New notes / practice problems (40 min)
Warm-Up:
What is 40% of 5/2?
What is 65% of ¾?
What is 80% of 7/12?
Pg. 356 #1 – #3, Pg. 356 #7 – #25 ALL
Quiz Thursday! 8

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

12. An equilateral polygon: All sides congruent.
An equiangular polygon: All angles congruent.
A regular polygon: All the sides and angles congruent.
Regular Polygon
Equilateral Polygon
Equiangular 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. Warm-Up: Pg. 356 #1 – #3, Pg. 356 #7 – #25 ALL
Wed, 2/5
SWBAT… find the sum of the measures of interior and exterior angles of a polygon.
Agenda
Warm-up (10 min)
Notes / practice problems (40 min)
Warm-Up:
Al is paid 35% as much as Franklin. If Franklin is paid $24.00 per hour, how much is Al paid per hour?
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! 15

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

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

18. Fri, 2/6
SWBAT… find the sum of the measures of interior and exterior angles of a polygon.
Agenda
Warm-up (10 min)
Notes / practice problems (40 min)
Warm-Up:
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?
Roman bought a shirt for $ 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 18

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. 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 = Sum
(n – 2)180 = 3600
180n – 360 = 3600
180n = 3960
n = 22 sides

22. 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 = Sum
(n – 2)180 = 2340
180n – 360 =
180n = 2,700
n = 15 sides

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

24. Ex. Find the values of the variables and the measures of the angles.
1300
900
1150

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
1350

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. Ex: Find the value of x Sum of exterior angles is 360°
(4x – 12) (3x + 13) = 360
7x = 360
– – 248
7x = 112
x = 12
(4x – 12)⁰
68⁰
60⁰
54⁰
(3x + 13)⁰
65⁰

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