Download 6.1 angles of polygons notes

6.1 angles of polygons 2016 ink.notebook
January 10, 2017
Page 11
Page 12
Page 10
Ch 6 Quadrilaterals
6.1 Angles in
Polygons
Page 13
Page 14
Lesson Objectives
Standards
Lesson Notes
6.1 Angles of Polygons
Press the tabs to view details.
1
6.1 angles of polygons 2016 ink.notebook
Lesson Objectives
Standards
Lesson Notes
After this lesson, you should be able to successfully recognize and apply angle relationships in polygons.
January 10, 2017
Lesson Objectives
Standards
Lesson Notes
G.MG.1 Use geometric shapes, their measures, and their properties to describe objects
Press the tabs to view details.
Post test
Pretest
number correct:
total number
of problems:
number correct:
total number
of problems:
Percentage correct:
Percentage correct:
difference
Change in percentage:
original
Quadrilaterals
=
2
6.1 angles of polygons 2016 ink.notebook
January 10, 2017
A ___________ polygon is equilateral and equiangular. This means that all of it's ________ and __________ are congruent
A segment joining any two nonconsecutive vertices is called a diagonal.
3
6.1 angles of polygons 2016 ink.notebook
January 10, 2017
4
6.1 angles of polygons 2016 ink.notebook
January 10, 2017
Polygon Interior Angle Sum Theorem
The sum of the interior angle measures of an n­sided convex polygon is (n − 2) · 180. Number of Sides:
Sum of Interior Angles:
n - gon
30­gon ­ 16­gon ­ Individual angle measure in
a regular triangle:
Number of Sides:
Sum of Interior Angles:
Individual angle measure in
a regular triangle:
5
6.1 angles of polygons 2016 ink.notebook
Find the value of x and the measure of each interior angle.
1.
January 10, 2017
Find the value of x and the measure of each interior angle.
2.
Find the SUM of the measures of the interior and exterior angles of each convex polygon.
3. decagon
4. 16­gon
5. 36­gon
6
6.1 angles of polygons 2016 ink.notebook
January 10, 2017
Find the measure of EACH interior AND exterior angle for each regular polygon.
6. hexagon
7. 20­gon
8. dodecagon
The measure of an interior angle of a regular polygon is given. Find the number of sides in the polygon.
360
# of sides =
180 - interior angle
9. 165
10. 144
11. 135
7
6.1 angles of polygons 2016 ink.notebook
January 10, 2017
There is a simple relationship among the exterior angles of a convex polygon.
12.
13.
8
6.1 angles of polygons 2016 ink.notebook
January 10, 2017
Practice
Find the SUM of the measures of the interior angles of each convex polygon.
1. nonagon
2. heptagon
3. decagon
4. 11­gon
5. 14­gon
6. 17­gon
The measure of an interior angle of a regular polygon is given. Find the number of sides in the polygon.
7. 108
8. 156
9. 120
10. 144
11. 160
12. 150
9
6.1 angles of polygons 2016 ink.notebook
Find the value of x and the measure of each interior angle.
13.
14.
January 10, 2017
Find the value of x and the measure of each interior angle.
15.
16.
Find the value of x and the measure of each interior angle.
Find the measures of each interior angle of each regular polygon.
17.
18. quadrilateral
19. pentagon
20. dodecagon
10
6.1 angles of polygons 2016 ink.notebook
Find the measure of EACH exterior angle for each regular polygon.
21. octagon
January 10, 2017
Find the measures of an exterior angle and an interior angle given the number of sides of each regular polygon. Round to the nearest tenth, if necessary.
24. 16
25. 30
26. 22
27. 24
28. 14
29. 40
22. nonagon
23. 12­gon
Find the measure of angle 1 in each diagram.
30.
31.
32. ARCHITECTURE In the Uffizi gallery in Florence, Italy, there is a room built by Buontalenti called the Tribune (La Tribuna in Italian). This room is shaped like a regular octagon.
La Tribuna
What angle do consecutive walls of the Tribune make with each other?
11
6.1 angles of polygons 2016 ink.notebook
January 10, 2017
Answers:
33. ARCHEOLOGY Archeologists unearthed parts of two adjacent walls of an ancient castle.
Before it was unearthed, they knew from ancient texts that the castle was shaped like a regular polygon, but nobody knew how many sides it had. Some said 6, others 8, and some even said 100. From the information in the figure, how many sides did the castle really have?
1. 1260 3. 1440 5. 2160 7. 5 9. 6 11. 18 13. 6x – 30 = 360, x = 65, mÚA = 115, mÚC = 115, mÚB = 65, mÚD = 65
15. 36x = 720, x = 20, mÚD = 140, mÚE = 140, mÚH = 140, mÚG = 140, mÚF = 80, mÚI= 80
17. 16x + 8 = 360, x = 22, mÚR = 128, mÚS = 52, mÚT = 128, mÚU = 52 19. 108 21. 45 23. 30 25. 168, 12
27. 165, 15 29. 171, 9 31. 55 33. 15 sides
In the book, do pages 394 – 397, problems: 8, 9, 30, 32
12
6.1 angles of polygons 2016 ink.notebook
January 10, 2017
13