Question

FIND THE NUMBER OF SIDES OF A REGULAR POLYGON ,THE SUM OF WHOSE INTERIOR ANGLE IS 1620 DEGRESS

Answer 1

11 sides... assuming all the angles are equal, number of angles=number of sides,now a triangle has 3 sides with sum of angles 180 degrees, quadrilateral which is made up of 2 triangles=180×2=360 degrees and so on..... so 1620÷180=9 and 9+2=11(since the multiple 1 represent a triangle,2 a quadrilateral and so on....so add 2 to multiple to get sides).... message if need help for understanding.

Answer 2

The number of edges (sides) is 'n'

The sum of all the interior angles of any regular polygon = ( n - 2 ) x 180
Therefore , ( n - 2 ) x 180 = 1620
( n - 2 ) = 1620 / 180
( n -2) = 9
n = 9 + 2
n = 11