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5.2 Exterior Angles of a Polygon

5.2 Exterior Angles of a Polygon. HOMEWORK: Lesson 5.2/1-10. Polygon Exterior  Sum Theorem. The sum of the measures of the exterior s of a polygon is 360°. Only one exterior  per vertex. 1. 2. 3. m 1 + m2 + m3 + m4 + m5 = 360. 5. 4.

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5.2 Exterior Angles of a Polygon

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  1. 5.2 Exterior Angles of a Polygon HOMEWORK: Lesson 5.2/1-10

  2. Polygon Exterior  Sum Theorem The sum of the measures of the exterior s of a polygon is 360°. • Only one exterior  per vertex. 1 2 3 m1 + m2 + m3 + m4 + m5 = 360 5 4 The interior  & the exterior  are Supplementary. Int + Ext = 180

  3. Polygon Exterior Angle-Sum Theorem Exterior • The sum of the measures of the angles of a polygon, one at each vertex, is ex: This pentagon has 5 sides. The sum of the 5 exterior angles is 360. 360.

  4. ONE Exterior Angle For Regular Polygons measure of One Exterior  =

  5. Example How many sides does each regular polygon have if its exterior angle is: a. 120 b. 24 360 24 360 120 = 15 = 3 15 sides 3 sides

  6. Exterior Angle Sum What is the measure of an interior angle of a regular octagon? (use the exterior angle) Solution: one ext = exterior angle = 45° interior angle = 180 – exterior angle interior angle = 180 – 45 = 135°

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

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

  9. Example Find x. 360˚ = x + 305 ˚ x = 360˚ – 305 ˚ = 55˚

  10. Example • How many sides does each regular polygon have if its exterior angle is: a. 120 b. 24 3 sides 15 sides

  11. Example • How many sides does each regular polygon have if its interior angle is: a. 90 b. 144 4 sides 10 sides

  12. Summary: SUM of the Interior Angles of a Polygon S = (n – 2) 180 OneInterior Angle of a REGULAR Polygon One= (n – 2) 180 n SUM of the Exterior Angles of a Polygon SE = 360 One Exterior Angle of a REGULAR Polygon OneEx= 360 n

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