Lesson 5.2 Polygon Exterior Angle Sum HOMEWORK: 5.2/ 1-10

2 Polygon Exterior Angle Sum Theorem The sum of the measures of the exterior angles of any polygon, one at each vertex is 360. m ∠1 + m∠2 + m∠3 + m∠4 + m∠5 = 360

Exterior angle sum = 360° If and Only if

Example: How many sides does a polygon have if it has an exterior  measure of 36°. = = 36n 10 = n

Example: Find the sum of the interior  s of a polygon if it has one exterior  measure of 24. = 24 n = 15 S = (n - 2)180 = (15 – 2)180 = (13)180 = 2340

Find x. Example Using exterior angle sum: Sum of the known exterior angles = 305 ° Exterior angle sum – 305 ° x = 360° – 305° = 55°

Example How many sides does each regular polygon have if its exterior angle is: a. 120  b. 24  Ext sum One angle sides triangle 15 sides = 3 = 15

Exterior Angles ONLINE! rangles.html rangles.html ry/parallel-and-perpendicular- lines/triang_prop_tut/v/sum-of-the-exterior- angles-of-convex-polygon ry/parallel-and-perpendicular- lines/triang_prop_tut/v/sum-of-the-exterior- angles-of-convex-polygon