Page 27 - TB_5B

Challenge Sum of Angles in a Polygon

1A. regular polygon can be divided into triangles. Find the relationship between

the number of triangles you can make and the number of sides a polygon
has. Learn how the sum of the angles in a polygon changes using the
relationship.

Draw a regular polygon. Divide the polygon into triangles.

1 180Ø = 180Ø 2 180Ø = 360Ø 3 180Ø = 540Ø 4 180Ø = 720Ø

Make a table.

Polygon Number of Number of Sum of the Interior Angles
Sides Triangles
Triangle
Quadrilateral 3 1 1 180 = 180Ø
4
Pentagon 5 2 2 180Ø = 360Ø
Hexagon 6
3 3 180Ø = 540Ø

4 4 180Ø = 720Ø

In a regular polygon, the number of triangles is always 2 less than the number
of sides. If the number of sides is n, the sum of the angles in a polygon is

(n 2 ) 180Ø.

1 . Find the measure of an angle in each polygon. If the number of sides of
a regular polygon is n, the
a. b. measure of an angle in a

polygon is

(n 2) 180Ø
n.

ØØ

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