7.3 & 7.4 Polygon Formulas completed.notebook January 10, 2014

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1 Chapter 7 Polygons Polygon 1. Closed Figure # of Sides Polygon Name 3 Triangle 4 Quadrilateral 5 Pentagon 6 Hexagon 2. Straight sides/edges 7 Heptagon 8 Octagon 9 Nonagon 10 Decagon 12 Dodecagon 15 Pentadecagon n n gon Polygon Formulas # Sides Sum of Angles Sum of Angles = number of sides If one exterior angles is drawn at each of the vertices, the sum of all the exterior angles is 360 o. Sum of Exterior Angles 1

2 # Sides Examples (Level 1) 1.) Find the sum of the angles in a decagon. # Diagonals 2.) Find the sum of the exterior angles in a heptaon. Number of Diagonals = number of sides 3.) Find the number of diagonals in a nonagon. Examples (Level 2) 4.) Find the name of the polygon whose angles add up to 1080 o. Bellringer: Given parallelogram ABCD with diagonals that meet at point O, if AO is 14 then what is the length of AC? 5.) Find the number of diagonals in a 100 gon. 6.) How many sides are in a polygon with angles adding up to 2065 o? Jan 9 11:10 AM 2

3 7.) A polygon with angles adding up to 1800 o has the number of sides it has cut in half. How many diagonals are in the new polygon? 8.) A hexagon has 4 angles with measures of 40 o, 100 o, 110 o, and 80 o. What is the measure of each of the remaining two angles if they are congruent to each other? 9.) What is the name of a polygon with 20 diagonals? Chapter 7 Polygons (Review) Polygon 1. Closed Figure 2. Straight sides/edges Regular Polygon = Polygon that is both equilateral and equiangular. 3

4 Regular Polygon = Polygon that is both equilateral and equiangular. Regular Polygon = Polygon that is both equilateral and equiangular. Quadrilateral Triangle Equilateral Equiangular Rhombus Equilateral Rectangle Equiangular Square Equiangular & Equilateral Regular Quadrilateral What do regular polygons allow us to do? Regular Polygon = Polygon that is both equilateral and equiangular. a.) What is the sum of the angles in a regular pentagon? Regular Pentagon b.) What is the measure of each angle in a regular pentagon? Pentagon Regular Pentagon c.) What is the sum of the exterior angles in a regular pentagon? d.) What is the measure of each exterior angle in a regular pentagon? Hexagon Regular Hexagon 4

5 In a regular polygon, the measure of each interior angle is defined as the sum of all the angles divided by the number of sides (which is the same as the number of angles). Measure of Each Interior Angle In a regular polygon, the measure of each exterior angle is defined as the sum of all the exterior angles divided by the number of sides. Measure of Each Exterior Angle Measure of Each Exterior Angle This formula also allows us to find the measure of each interior angle in a slightly different way. Interior and exterior angles at the same vertex are supplementary to each other. So, you can find the measure of each exterior angle. Then, find its supplement to determine the measure of the interior angle. Jan 10 11:21 AM 5

6 Jan 10 1:57 PM Jan 10 11:34 AM Summary of all Formulas #1 3 Apply to all polygons 1.) Sum of Interior Angles 2.) Sum of Exterior Angles 3.) Number of Diagonals #4 5 Apply to only regular polygons 4.) Measure of Each Interior Angle 5.) Measure of Each Exterior Angle Jan 10 11:40 AM 6

7 10.) Use two different ways to find the measure of each interior angle in a regular hexagon. 11.) Find the name and number of diagonals in a regular polygon whose interior angles measure 160 o. Jan 10 11:56 AM 7

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