GeometrySection 8.1

Find Angle Measures in Polygons

Angle Sums in PolygonsPOLYGON # OF SIDES # OF TRIANGLES Sum of the

measures of interior angles

Triangle

Quadrilateral

Pentagon

Hexagon

Heptagon

Octogon

Polygon Interior Angles Theorem The sum of the measures of the interior

angles of a convex n-gon is:(n – 2) · 180°

(number of sides – 2) times 180°

Interior Angles of a Quadrilateral The sum of the measures of the interior

angles of a quadrilateral is 360°

Examples1. Find the sum of the measures of the interior angles of an

11-gon

2. The sum of the measures of the interior angles of a convex polygon is 1440°. Classify the polygon by the number of sides.

Polygon Exterior Angles Theorem The sum of the measures of the exterior

angles of a convex polygon , one angle at each vertex, is 360°.

Example A convex hexagon has exterior angles with

measures 34°, 49°, 58°, 67°, and 75°. What is the measure of an exterior angle at the sixth vertex?

Assignment Section 8.1 Page 510 Problems # 4 - 24 even, 28, 30