2. 8.2 Angles in Polygons

3. Polygon Number of sides Number of triangles Sum of measures of interior angles Triangle Quadrilateral Pentagon Hexagon Heptagon 3 4 1 1·180°=180° 2 2·180°=360° 5 3 3·180°=540° 6 4 4·180°=720° 75 5·180°=900°

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

5. Interior or Exterior?

6. Theorem 8.1: The sum of the measures of the interior angles of a convex polygon with n sides is ˚. 1 2 3 4

7. 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.

8. 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.

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

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