Question

The measure of an interor angle of a regular polygon is given. Find the number of sides in the polygon.

Answer 1

Let side be n

#1

$\\ \sf\longmapsto 120n=(n-2)180$

$\\ \sf\longmapsto 120n=180n-360$

$\\ \sf\longmapsto -60n=-360$

$\\ \sf\longmapsto n=6$

#2

$\\ \sf\longmapsto 160n=(n-2)180$

$\\ \sf\longmapsto 160n=180n-240$

$\\ \sf\longmapsto -20n=-240$

$\\ \sf\longmapsto n=12$

#3

$\\ \sf\longmapsto 144n=(n-2)180$

$\\ \sf\longmapsto 144n=180n-360$

$\\ \sf\longmapsto -36n=-360$

$\\ \sf\longmapsto n=10$