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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
