3-5 Angles of a Polygon

A) Terms Polygons – each segment intersects exactly two other segments, one at each endpoint. Are the following figures a polygon? Yes or No

Kinds of Polygons. 1) Regular Polygon - is a polygon that is equilateral and equiangular 2) Convex Polygon - is a polygon that no line that contains a side of the polygon contains a point in the interior of the polygon. 3) Concave Polygon or Nonconvex Polygon - is a polygon whose side or sides are indented, where a line drawn through a side cuts through the polygon figure.

Name the polygons you know based on their sides. Number of sides Type of Polygon

4) Diagonal – is a segment joining two nonconsecutive vertices. Ex.

Theorems: Theorem 3 – 13 The sum of the measure of the angles of a convex polygon with n sides is (n – 2) 180 Ex. Find the measure of one Pentagon angle.

Theorem The sum of the measures of the exterior angles of any convex polygon, one angle at each vertex is 360° Ex. Find the measure of each exterior angle.

Ex. 2 Find the interior angle sum and the exterior angle for: 1) Triangle: 2) 20 – gon 3) 27 - gon

Ex. 3 An exterior angle of a regular polygon has measure 10. The polygon has _______sides. Ex. 4 An interior angle of a regular polygon has measure 160. The polygon has _____sides. Ex. 5 Three of the angles of a quadrilateral have measures 90, 60, and 115. The fourth angle has measure__________.