8.2 Angles in Polygons Polygon Number of sides Number of triangles Sum of measures of interior angles Triangle Quadrilateral Pentagon Hexagon Heptagon.

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Presentation transcript:

8.2 Angles in Polygons

Polygon Number of sides Number of triangles Sum of measures of interior angles Triangle Quadrilateral Pentagon Hexagon Heptagon ·180°=180° 2 2·180°=360° 5 3 3·180°=540° 6 4 4·180°=720° 75 5·180°=900°

Angle Review  Polygons have two types of angles Interior angles Exterior angles

Interior or Exterior?

Theorem 8.1: The sum of the measures of the interior angles of a convex polygon with n sides is ˚

Example Find the measure of the interior angle of a regular hexagon. The sum of the measures of the hexagon is: Since the hexagon is regular, each angle has the same measure. Hence, divide by 6 to find the measure of one angle.

Example Find the measure of angle E. Find the sum of the measures of any pentagon. AB C D E Subtract the sum of the given angles from this total.

Theorem 8.2: The sum of the measures of the exterior angles of a convex polygon, one angle at each vertex, is 360˚.

Example Find the value of x. x˚ 65˚ 44˚ 75˚ 54˚ 76˚ 65˚+44 ˚ +75 ˚ +54 ˚ +76 ˚ =314˚360˚-314 ˚ =46˚