5.2 Exterior Angles of a Polygon

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Presentation transcript:

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 The interior  & the exterior  are Supplementary. Int + Ext = 180

Polygon Exterior Angle-Sum Theorem 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. Exterior 360.

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

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

Exterior Angle Sum What is the measure of an interior angle of a regular octagon? (use the exterior angle) Solution: one ext  = 360 8 exterior angle = 45° interior angle = 180 – exterior angle interior angle = 180 – 45 = 135°

𝑛= 𝑒𝑥𝑡 𝑠𝑢𝑚 𝑜𝑛𝑒 = 360° 36° = 10 sides Example: How many sides does a polygon have if it has an exterior  measure of 36°. 𝑛= 𝑒𝑥𝑡 𝑠𝑢𝑚 𝑜𝑛𝑒 = 360° 36° = 10 sides 𝑛=10 𝑠𝑖𝑑𝑒𝑠

Example: S = (n - 2)180 = (15 – 2)180 = (13)180 S = 2340° Find the sum of the interior s of a polygon if it has one exterior  measure of 24°. 𝑛= 𝑒𝑥𝑡 𝑠𝑢𝑚 𝑜𝑛𝑒 𝑛= 360 24 = 15 sides S = (n - 2)180 = (15 – 2)180 = (13)180 S = 2340°

Example 360˚ = x + 305 ˚ x = 360˚ – 305 ˚ = 55˚ Find x. 90+45+80+90=305

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

Example How many sides does each regular polygon have if its interior angle is: a. 90 b. 144 𝐸𝑎𝑐ℎ= 𝑛−2 180° 𝑛 𝐸𝑎𝑐ℎ= 𝑛−2 180° 𝑛 144°= 𝑛−2 180° 𝑛 90°= 𝑛−2 180° 𝑛 90°𝑛= 𝑛−2 180° 144°𝑛= 𝑛−2 180° 90°𝑛=180°𝑛−360 144°𝑛=180°𝑛−360 −36°𝑛=−360 −90°𝑛=−360 𝑛= 4 sides 𝑛= 10 sides

Summary: SUM of the Interior Angles of a Polygon S = (n – 2) 180 One Interior 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