In a circle with centre O, AOC is the diameter. B is a point on the circumference of the circle such that arc AB is 1/5 of the arc BC. What is the degree measure of ∠BOC?

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Given: AOC is the diameter of the circle, so arc AOC is 180°. Points A, B, C lie on the circumference.

Let the measure of arc AB be x degrees.
Then arc BC = 5x (since arc AB is 1/5 of arc BC).

Since AOC is a diameter, the total arc from A to C passing through B is arc AB + arc BC = x + 5x = 6x.
But arc AOC = 180°, so 6x = 180° ⇒ x = 30°.

Therefore, arc AB = 30°, arc BC = 150°.

Angle BOC is the central angle subtending arc BC, so ∠BOC = arc BC = 150°.

Hence, the degree measure of ∠BOC is 150°.

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