Question

Find the measure of each exterior angle of a regular Pentagon
Hexagon
Heptagon
Decagon
polygon of 15 sides
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Answer 1

Answer:

Step-by-step explanation:-

(i) In a regular pentagon, all sides are same size and measure of all interior angles are Same. The sum of interior angles of pentagon is (n-2) × 180o where n is the number of sides of polygon. (5-2) × 180o = 540o here n=5 because penta means 5 Each interior angle= 540/5 = 108o As we know that the sum of interior and exterior angle is 1800 Exterior angle + interior angle = 1800 Exterior angle + 108o= 1800 Exterior angle = 1800– 108o= 720 (ii) In a regular hexagon, all sides are same size and measure of all interior angles are Same. The sum of interior angles of pentagon is (n-2) × 180o where n is the number of sides of polygon. (6-2) × 180o = 720o here n=6 because hexa means 6 Each interior angle= 720/6 = 120o As we know that the sum of interior and exterior angle is 1800 Exterior angle + interior angle = 1800 Exterior angle + 120o= 1800 Exterior angle = 1800– 120o= 600 (iii) In a regular heptagon, all sides are same size and measure of all interior angles are Same. The sum of interior angles of heptagon is (n-2) × 180o where n is the number of sides of polygon. (7-2) × 180o = 900o here n=7 because hepta means 7 Each interior angle= 900/7 = 128.57o As we know that the sum of interior and exterior angle is 1800 Exterior angle + interior angle = 1800 Exterior angle + 128.57o= 1800 Exterior angle = 1800– 128.57o= 51.430 (iv) In a regular decagon, all sides are same size and measure of all interior angles are Same. The sum of interior angles of decagon is (n-2) × 180o where n is the number of sides of polygon. (10-2) × 180o =1440o here n=10 because deca means 10 Each interior angle= 1440/10 = 144o As we know that the sum of interior and exterior angle is 1800 Exterior angle + interior angle = 1800 Exterior angle + 144o= 1800 Exterior angle = 1800– 144o= 360 (v) In a regular polygon, all sides are same size and measure of all interior angles are Same. The sum of interior angles of polygon of 15 sides is (n-2) × 180o where n is the number of sides of polygon. (15-2) × 180o =1440 o here n=15 Each interior angle= 2340/15 = 156o As we know that the sum of interior and exterior angle is 1800 Exterior angle + interior angle = 1800 Exterior angle + 156o= 1800 Exterior angle = 1800– 156o= 240