1. Interior Angle Sum = ( n – 2 )( 180° ) Find the interior angle sum of each polygon. ( 4 – 2 ) 180°= ( 2 ) 180°= 360° ( 6 – 2 ) 180°= ( 4 ) 180°= 720° 1) Quadrilateral 2) Hexagon Find the measure of one interior angle. Assume the polygon is regular. 3) Decagon( 10 – 2 ) 180°= ( 8 ) 180°= 1440° 4) Pentagon( 5 – 2 ) 180°= ( 3 ) 180°= 540° 540° ÷ 5= 108° 5) Octagon ( 8 – 2 ) 180°= ( 6 ) 180°= 1080° 1080° ÷ 8= 135°

2. 16.03 Exterior Angle Sum of a Polygon

3. An exterior angle is formed by extending a side of the polygon. A B CD Notice: The sum of one interior angle and one exterior angle equals 180°. E F The angles are supplementary.

4. A B C D Each side of the polygon can be extended, therefore the number of exterior angles and interior angles are the same. E Imagine walking around the polygon. At each vertex, one has to turn the number of degrees in each exterior angle. It’s like walking around in a circle.

5. That means you have turned 360° This will be true for any polygon, no matter how many sides. Therefore we can say for any polygon, the sum of the exterior angles will always equal 360°. Find the sum of the exterior angles of a: Hexagon360° Octagon360° Decagon 360°

6. Find x in each figure. 115°75° 120° x°x° 115 + 75 + 120 + x = 360 310 + x = 360 x = 50 x°x° 150° 140° 140 + 150 + x = 360 290 + x = 360 x = 70

7. A B C D If the polygon is regular, the measure of one exterior angle can be found by dividing 360° by the number of sides. E 360° ÷ 5 Find the measure of one exterior angle in each of the following polygons. = 72° Octagon 360° ÷ 8= 45° Dodecagon360° ÷ 12= 30°