Question

calculate the number of sides of a regular polygon if (a) each exterior angle of a polygon is 24° (b) each interior angle of the polygon is 162°​

Answer 1

Answer:

(a) 15 (b) 30

Step-by-step explanation:

(a) As we know sum of all exterior angle is 360 degree the no find number of sides (equation 1)

X = number of sides

therefore

x=360/24

x=15

Therefore sides are 15

(b) as we know sum of adjacent angles =180

Then interior angle +exterior angle =180

162+exterior angle = 180

exterior angle = 12

X = 360/12. from equation 1

x=30

Therefore number of sides =30

Answer 2

Answer:

(a) The formula for finding the measure of an exterior angle of a regular polygon is  360/ n  , where  n  is the number of sides of the polygon. So,

24  =  360/ n

24 ( n )  = n ( 360/ n  )

24 n  = 360

24 n/ 24   =  360 /24

 n  =  15

So the polygon has  15  sides.

(b)  a polygon has interior angles of  162°  . It is assumed from this that all interior angles are  162°   .  As interior angles are  162°  , each exterior angle is  

180° -  162° =  18°  

 Sum of all the exterior angles of a polygon is always  

360°   and as each exterior angle is  18°  ,

Number of angles / sides of polygon are  

360°/ 18°

=20

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