Question

In the given figure, O is the centre of the circle. AB is the side of a square, BC is the side of a regular pentagon and CD is the side of a regular hexagon. Find angle BCD.

Answer 1

Answer:

114°

Step-by-step explanation:

Since, BC is the side of a regular pentagon, BC will subtend an angle of 2π/5° at O=72°, so ∠OCB + ∠OBC = 108°, But ∠OCB = ∠OBC, hence

∠OCB = 54°

Since, CD is the side of a regular hexagon, CD will subtend an angle of 2π/6° at O=60°, so ∠OCD + ∠ODC = 120°, But ∠OCB = ∠OBC, hence

∠OCD = 60°

Now, ∠BCD = ∠OCB + ∠OCD = 114°.