Understanding Exterior Angles in Polygons
Learn how to calculate exterior angles in polygons, understand the relationship between interior and exterior angles, find the size of exterior angles in different types of polygons, and determine the number of sides in a regular polygon based on its exterior angles.
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12 June 2025 The exterior angles of a polygon. LO: To calculate the exterior angles in a polygon. www.mathssupport.org
Exterior angles in polygons When we extend the sides of a polygon outside the shape exterior angles are formed. www.mathssupport.org
The sum of exterior angles in a polygon For any polygon, the sum of the interior and exterior angles at each vertex is 180 . For n vertices, the sum of n interior and n exterior angles is n 180 or 180n . The sum of the interior angles is (n 2) 180 . We can write this algebraically as 180(n 2) = 180n 360 . www.mathssupport.org
The sum of exterior angles in a polygon If the sum of both the interior and the exterior angles is 180n and the sum of the interior angles is 180n 360 , the sum of the exterior angles is the difference between these two. The sum of the exterior angles = 180n (180n 360 ) = 180n 180n + 360 = 360 The sum of the exterior angles in a polygon is 360 . www.mathssupport.org
Polygons Calculate the size of the exterior angles of these regular polygons. There are 5 exterior angles and all are equal = 360 5 = 72 There are 7 exterior angles and all are equal = 360 7 = 51.4 There are 6 exterior angles and all are equal There are 8 exterior angles and all are equal = 360 6 = 60 = 360 8 = 45 www.mathssupport.org
Polygons Find the size of each exterior angle in this polygon All exterior angles add up to 360 . (3x 10) (x + 20) x x x = 360 + + + + 50 x (7x + 10) = 360 x 50 (x + 20) (7x) = 350 (3x 10) 140 x 50 (50 + 20) x = 50 (x + 20) 70 70 (3x 10) (3(50) 10) 140 www.mathssupport.org
Polygons Find the number of sides of a regular polygon whose exterior angle is 12 . All the exterior angles in a regular polygon are equal All the exterior angles in a regular polygon add up to 360 = 360 12 = 30 So, the polygon has 30 equal sides www.mathssupport.org
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