Question

In the given figure, AB is a side of a regular hexagon and AC is a side of a regular eight sided polygon. Find angle OBC
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Answer 1

Step-by-step explanation:

angle AOB = 360°/6 => 60° [ interior angle of regular hexagon is 60° ]

angle AOC = 360°/8 => 45° [ interior angle of regular eight sided polygon is 45° ]

there angle BOC = 60° + 45° => 105°

in ∆ OBC, OB = OC [ radii ]

hence angle OBC = angle OCB -----------(1)

=> angle OBC + angle OCB + angle BOC = 180°

=> 2 angle OBC + 105° = 180°

=> 2 angle OBC = 180° - 105°

=> 2 angle OBC = 75°

therefore angle OBC = 75°/2 => 37.5°