Interior-and-Exterior-Angles-of-Polygons.ppt
- 1. Interior and Exterior Angles of Polygons
- 2. Diagonals A diagonal of a polygon is a segment that joins two nonconsecutive vertices. Ex. 1. How many diagonals can we draw in the rectangle?
- 3. Triangles…… Ex. 2. How many diagonals can be drawn in the triangle? Why?
- 4. What is the sum of the interior angles of a triangle? Ex. 3. Find the missing angles. 3xº xº 72º A B C m<A = m<B =
- 5. Quadrilaterals… In each quadrilateral draw all possible diagonals from Vertex A. How many triangles were formed as a result? What do you think this means for the sum of the interior angles of a quadrilateral?
- 6. Pentagons…. In the following pentagon draw all possible diagonals from Vertex A. How many triangles were formed as a result? What do you think this means for the sum of the interior angles of a quadrilateral?
- 7. Polygons…. Now take a second and draw in all diagonals from one vertex of each polygon on your worksheet. Is there a relationship between the sides and the number of triangles? Hexagon Nonagon Octagon Decagon
- 8. Sum of the interior angles of a convex polygon. SI = (n – 2) • 180 Ex. 4. Find the sum of the interior angles of a convex heptagon. Ex. 5. Find the sum of the interior angles of a convex 15-gon.
- 9. Ex. 6. Solve for x. Ex. 7. Solve for y. Not drawn to scale 120º 48º xº 2xº 5yº 9yº 92º 139º 71º
- 10. Regular Polygons A REGULAR polygon is Equilateral and Equiangular (all sides and all angles ). To Find the measure of each Interior Angle of a regular convex polygon. ( 2) 180 n n
- 11. Ex. 8. Find the measure of each angle in a regular convex octagon. Ex. 9. The measure of each interior angle of a regular polygon is 165º. How many sides does the polygon have?
- 12. Exterior Angles The Exterior Angle of any polygon forms a linear pair with an Interior angle of a polygon. Ex. <1 is an exterior angle. <1 and <2 form a linear pair. <1 <2 m<1 + m<2 = 180
- 13. Sum of the exterior angles of a convex polygon. 360º ALL Exterior Angles of EVERY polygon add up to 360º
- 14. Ex. 10. What is the sum of the exterior angles of a convex triangle? Ex. 11. What is the sum of the exterior angles of a convex 300-gon?
- 15. Regular Polygons To Find the measure of each Exterior Angle of a regular convex polygon. 360 n
- 16. Ex. 12. Find the measure of each exterior angle of a regular heptagon. Ex. 13. The measure of each exterior angle of a regular polygon is 40º. How many sides does it have?