1. 8 th Grade Math POLYGONS

2. A polygon is a plane figure with at least three straight sides and angles, and typically five or more. WHAT IS A POLYGON?

3. A polygon with n-sides is called an n-gon. It is a general term to stand for all types of polygons. N-GON

4. An interior angle is an angle inside a shape INTERIOR ANGLES OF POLYGONS

5. The interior angles of a triangle add up to 180° TRIANGLES

6. A quadrilateral has 4 straight sides. The interior angles of a quadrilateral add up to 360° QUADRILATERALS

7. A pentagon has 5 sides. The interior angles of a pentagon add up to 540° PENTAGON A B C D E A + B + C + D + E = 540°

8. (n-2)  180°= Sum of Angles TO FIND THE ANGLES OF A POLYGON WE USE THIS FORMULA N is the number of sides

9. Each time we add a side (triangle to a quadrilateral, quadrilateral to a pentagon, etc.) we add another 180° to the total THE GENERAL RULE

10. SHAPESIDESSUM OF INTERIOR ANGLES Triangle3180° Quadrilateral4360° Pentagon5540° Hexagon6720° Heptagon (or Septagon)7900° Octagon81080° Nonagon91260° Decagon101440° Hendecagon111620° Dodecagon121800°

11. FIND THE SUM OF THE MEASURES OF THE ANGLES IN A NONAGON How many sides does a nonagon have? 9 What formula do I use to find the sum of the measures of the angles? (n-2)180° Now what do I do?Substitute the 9 for n (9-2) 180° = (7) 180° = 1260°

12. FIND THE MISSING ANGLE 100 ° 145° 35° First, find what the sum of the angle measurements should be. What formula do I use? (n-2)180° (5-2)180 ° = 540° NOW WHAT? X 540 100 35 100 -145 160X =°

13. FIND THE NUMBER OF SIDES IN THE POLYGON WHOSE ANGLE MEASURES HAVE THE GIVEN SUM OF 360° What formula do I need to use? (n-2)  180° = SUM OF ANGLES 360° Now solve for n (n-2)180 = 360 (n-2) = 360/180 (n-2) = 2 n=4 Solve for n Divide both sides by 180 Add 2 to both sides

14. ANY QUESTIONS?

15. REFERENCES www.edgenuity.com http://www.mathsisfun.com/geometry/interior-angles-polygons.html http://www.regentsprep.org/Regents/math/geometry/GG3/LPoly1.htm