Octagon:
= [(8-2)×180]÷8
= 135
Angle of LMN is:
= 360-135-60
= 165
Angle of EMN is:
= 180÷3
= 60
The number of side is :
[(n-2)×180]÷n = 165
(180n-360)÷n = 165
180n-360 = 165n
180n-165n = 360
15n = 360
n = 360÷15
n = 24
So, the number of side of the regular polygon R is 24.
