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# 1-25/10 Interior and Exterior Angles

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### 1-25/10 Interior and Exterior Angles

1. 1. Polygons And so it begins
2. 2. <ul><li>If the segments of a polygon are turned into lines and at least one line hits another side then the shape is said to be concave </li></ul><ul><li>A polygon is convex if any line drawn through the polygon only intersects two sides. </li></ul><ul><li>Concave and Convex are opposites </li></ul>
3. 3. <ul><li>The angles on the inside of a polygon are called Interior Angles </li></ul><ul><li>An Exterior Angle is the angle made by turning a side into a ray then measuring the angle between the ray and its closest side </li></ul>
4. 4. Sum of interior angles Find a function [ f(n) = something ] that maps the relationship between the number of sides and the sum of the interior angles. If you think you’ve found it then make sure you can plug in the other sides of the table and get the resultant angle sum 1 4 7 8 2 3 5 6 Your Name Here Shape triangle quadrilateral Pentagon Hexagon 15-gon Sum of Interior Angles 180° 360° 540° 720° 2340°
5. 5. The official math formula <ul><li>Sum of interior angles = (n – 2)•180 </li></ul><ul><li>What is the sum of interior angles of a 12-gon? </li></ul><ul><li>If a polygon has interior angles that sum to 4140° how many sides does it have? </li></ul>
6. 6. What is the sum of interior angles of a 12-gon?
7. 7. If a polygon has interior angles that sum to 4140° how many sides does it have?
8. 8. Exterior Angle Sum <ul><li>If a polygon is convex, then the Exterior Angles always sum to 360° </li></ul><ul><li>Weird huh? </li></ul>
9. 13. Regular Polygons <ul><li>Regular means that all sides are all the same size and all angles are the same measure. </li></ul><ul><li>Regular polygons are always convex </li></ul>