Question

if one side of a regular pentagon is 6cm find the length of its diagonal [sin18=0.31]​

Answer 1

Answer:

ABCDE is a pentagon. Hence, ∠EDC=108

∘

(Interior angle of a pentagon)

Also, ∠EDF=90

∘

Now, ∠CDF=360

o

−∠EDF−∠EDC

∠CDF=360

o

−90

o

−108

o

=162

o

Now, Interior angle of a polygon,

n

180

o

(n−2)

=162

o

180n−360=162n

18n=360

n=20

Thus, polygon has 20 sides.