The correct option is D 3π5
Interior angle of a n sided regular polygon is n−2n×180∘
For a pentagon, n=5
⇒ Magnitude of Interior angle =5−25×180∘=35×180∘=108∘
Now, Using the relation:
D180∘=Rπ
⇒R=π×D180∘
⇒R=π×108∘180∘=3π5
Hence, magnitude of interior angle of a pentagon =3π5
Similarly, for an octagon n=8
⇒ Magnitude of Interior angle =8−28×180∘=68×180∘=135∘
Now, Using the relation:
D180∘=Rπ
⇒R=π×D180∘
⇒R=π×135∘180∘=3π4
Hence, magnitude of interior angle of an octagon =3π4