in your journal, create this chart polygonnumber of angles sum of degrees place your tan homework on...
TRANSCRIPT
In your journal, create this chart
Polygon Number of Angles
Sum of degrees
Place your tan homework on your desk
Expectations
• Explain how the formula for the sum of angles of a polygon is derived
• Compute problems regarding the sum of angles of a polygon
How many degrees in the sum of the interior angles of a triangle?
180 Degrees
Add the data to the chartPolygon Number
of AnglesSum of degrees
Triangle 3 180
How many degrees in the sum of the interior angles of a quadrilateral?
360 Degrees
Add the data to the chartPolygon Number
of AnglesSum of degrees
Triangle 3 180Quadrilateral 4 360
How many degrees in the sum of the interior angles of a pentagon?
330 + 210 =
540
Add the data to the chartPolygon Number
of AnglesSum of degrees
Triangle 3 180Quadrilateral 4 360Pentagon 5 540
Add the data to the chartPolygon Number
of AnglesSum of degrees
Triangle 3 180Quadrilateral 4 360Pentagon 5 540Hexagon 6 710
Add the data to the chartPolygon Number
of AnglesSum of degrees
Triangle 3 180Quadrilateral 4 360Pentagon 5 540Hexagon 6 710Heptagon 7 890
Look for a patternPolygon Number
of AnglesSum of degrees
Triangle 3 180Quadrilateral 4 360Pentagon 5 540Hexagon 6 710Heptagon 7 890
+ 180
+ 180+ 180
+ 180
The sum of the degrees increases 180 degrees for every additional
angle
Look for a patternPolygon Number
of AnglesSum of degrees
Triangle 3 180Quadrilateral 4 360Pentagon 5 540Hexagon 6 710Heptagon 7 890
What is the relationship between the number multiplied by 180 and number of sides of a
triangle?2 x 180 =3 x 180 =
4 x 180 =
5 x 180 =
1 x 180 =
Look for a patternPolygon Number
of AnglesSum of degrees
Triangle 3 180Quadrilateral 4 360Pentagon 5 540Hexagon 6 710Heptagon 7 890
What is the relationship between the number multiplied by 180 and number of sides of a
triangle?
2 x 180 =3 x 180 =
4 x 180 =
5 x 180 =
1 x 180 =or
Number of angles – 2 times 180 = sum of degrees
(n-2)180 = Sum of degrees
What is the sum of all the angles of an octagon?
(n-2)180 = Sum of degrees
(8-2)180 = Sum of degrees
6 x 180 = 1080
What is the sum of all the angles of an nonagon?
(n-2)180 = Sum of degrees
(9-2)180 = Sum of degrees
7 x 180 = 1260
Record formula in journalPolygon Number
of AnglesSum of degrees
Triangle 3 180Quadrilateral 4 360Pentagon 5 540Hexagon 6 710Heptagon 7 890
(n-2)180 = Sum of degrees