Question

In the figure, a regular octagon and a regular pentagon are put together. The measure of ∠ABC is

117∘

127∘

107∘

171∘

• A. ${171}^{\circ }$
• B. ${117}^{\circ }$
• C. ${127}^{\circ }$
• D. ${107}^{\circ }$

Answer 1

The correct option is B

${117}^{\circ }$

For regular pentagon, n=5.

⇒ Each exterior angle =360/5=72∘

=72∘

Now, e+i=360∘ (Linear pair)

72+i=180∘

⇒i=108∘

For a regular octagon, n=8.

∴ Each exterior angle =360/8=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∘