The figure shows a regular pentagon and equilateral triangles are put together. Then which of the following statements are true?
∠ABC=132∘
∠ABC=∠CDE=∠EFG
∠BDF=108∘
For regular pentagon, n=5.
⇒ Each exterior angle =3605=72∘
=72∘
Now, e+i=360∘ (Linear pair)
72+i=180∘
⇒i=108∘
⇒∠BDF=108∘
Each angle of an equilateral triangle is 60∘
Now, 60∘+108∘+60∘+∠ABC=360∘...(Angles around a point)
⇒228∘+∠ABC=360∘
⇒∠ABC=360∘−228∘
⇒∠ABC=132∘
Also, ∠ABC=∠CDE=∠EFG