F.2 maths (Plane Geometry)

a. Let the number of sides of a regular polygon is n.
(n-2)*180=144n
180n-360=144n
180n-144n=360
36n=360
n=10
There are 10 sides of this polygon.
b. Let the number of sides of a regular polygon is p.
(p-2)*180=160p
180p-360=160p
180p-160p=360
20p=360
p=18
There are 18 sides of this polygon.
c. Let the number of sides of a regular polygon is s.
(s-2)*157.5=157.5s
180s-315=157.5s
180s-157.5s=360
22.5s=360
s=16
There are 16sides of this polygon.

Let n be the number of sides of the polygon
(a) [(n-2)x180]/n=144
180(n-2)=144n
180n-360=144n
36n=360
n=10

(b)[(n-2)x180]/n=160
180(n-2)=160n
180n-360=160n
20n=360
n=18

(c)[(n-2)x180]/n=157.5
180(n-2)=157.5n
180n-360=157.5n
22.5n=360
n=16

P.S. (n-2)x180係angle sum of polygon
將佢除以n就會係每隻內角我度數

希望可以幫到你啦~^^