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Question

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


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Solution

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=18045

i=135

Now, 135+108+ABC=360 (Angles around a point)

ABC+243=360

ABC=360243

=117


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