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