In the figure, a regular octagon and a regular pentagon are put together. The measure of ∠ABC is
For regular pentagon, n=5.
⇒ Each exterior angle =3605=72∘
=72∘
Now, e+i=360∘ (Linear pair)
72+i=180∘
⇒i=108∘
For a regular octagon, n=8.
∴ Each exterior angle =3608=45∘
Now, i+e=180∘ (Linear pair)
⇒i+45∘=180∘
⇒i=180∘−45∘
⇒i=135∘
Now, 135∘+108∘+∠ABC=360∘ (Angles around a point)
⇒∠ABC+243∘=360∘
⇒∠ABC=360∘−243∘
=117∘