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-#3Quiz Thursday!
Mon, 2/3
The sum of the interior measures of the angles of a triangle is 180 degrees.
Triangle Sum Theorem
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
Review HW:Page 175: #1 – #21 ALL
Page 177: #29 – #32 ALL
Exit Slip: ½ sheet – Collected1.) Find the value of x, y, and z?
3.) Find m<1 and m<2.2.) Find the value of x
Summary
Be VERY specific!1. Sum of interior angles of a triangle = 1800
2. Exterior angle = Sum of interior angles in triangle
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 ¾?
3. What is 80% of 7/12?
Pg. 356 #1 – #3, Pg. 356 #7 – #25 ALLQuiz Thursday!
Tues, 2/4
Chapter 6.1 Polygon Angle – Sum
Polygon
A closed plane figure formed by 3 or more segments that all lie in one plane
Polygons are named by number of sidesNumber of Sides Polygon
34
5
6
78
9
10
12
n
TriangleQuadrilateral
Pentagon
Hexagon
Heptagon
Octagon
Nonagon
Decagon
Dodecagon
n-gon
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
Concave
If any part of a diagonal contains points in the exterior of the polygon.
Convex If no diagonal contains points in the exterior.
A regular polygon is always convex.
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 ALLQuiz Tomorrow!
Wed, 2/5
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°
Ex: What is the measure of angle Y in pentagon TODAY?
(5 2) 180m T m O m D m A m Y
110 90 120 150 3 180m Y 470 540m Y
70m Y
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
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
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°
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 = 3600180n – 360 = 3600 + 360 + 360 180n = 3960 180 180 n = 22 sides
(n – 2)180 = Sum
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 = 2340180n – 360 = 2340 + 360 + 360 180n = 2,700 180 180 n = 15 sides
(n – 2)180 = Sum
4x – 2
82
108
2x + 10108 + 82 + 4x – 2 + 2x + 10 = (4 – 2)180
6x + 198 = 3606x = 162 6 6
x = 27
Ex: Solve for x
Sum = (n – 2)180
Ex. Find the values of the variables and the measures of the angles.
x = 251300
900
1150
1150
900
The measure of each interior angle of a regular n-gon is ( 2) 180
.n
n
Ex: What is the measure of each or one interior angle in a regular octagon?
( 2) 180.
n
n
(8 – 2)180 / 8
1350
What do you notice about the exterior angles of the polygons below?
Polygon Exterior Angle-Sum Theorem
The sum of the measures of the exterior angles of a polygon, one at each vertex, is 360.
1 2 3 4 5 360m m m m m
Ex. Find the exterior angle sum of a decagon.
54⁰
68⁰
65⁰
(3x + 13)⁰
60⁰
(4x – 12)⁰
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
Ex: What is the measure of angle 1 in the regular octagon?
3601
8m
1 45m