Question

each interior angle of a regular polygon is 140degree
find the interior angle of a regular polygon which has doubled the number of sides as the first polygon

Answer 1

interior ang = 140

exterior ang =180-140=40

no.of sides =360/40 =9

if sides are doubled then no. of sides =18

each interior angle = (n-2)*180/n =(18-2)180/18

=16×10=160

Answer 2

sum of all interior angles of a polygon = (n-2)180 where n is no. of sides
therefore measure of each angle = [(n-2)180]/n
therefore,

$140 = \frac{(n - 2)180}{n} \\ 140n = 180n - 360 \\ 180n - 140n = 360 \\ 40n = 360 \\ n = 9$

therefore the polygon has 9 sides
.·. new polygon has 18 sides
sum of internal angles = (n-2)180
.·. measure of each internal angle
= [(n-2)180]/18

$\frac{(18 - 2)180}{18} = 16 \times 10 = 160$

therefore each internal angle measures 160°.