Question

ABCDE is a regular pentagon with sides of length 6 cm. CD is also a side of a regular polygon with n sides. Given that ∠EDF = 90°, find n.

(a) 18

(b) 10

(c) 20

(b) 12

Answer 1

Correct option is (c) 20

ABCDE is a pentagon. Hence, ∠EDC = 108^∘ (Interior angle of a pentagon)

Also, ∠EDF = 90^∘

Now, ∠CDF = 360^∘ − ∠EDF − ∠EDC

∠CDF = 360^∘ − 90^∘ − 108^∘ = 162^∘

Now, Interior angle of a polygon,

\(\frac{180°(n-2)}n = 162°\)

180n − 360 = 162n

18n = 360

n = 20

Thus, polygon has 20 sides.