Multiple choice

An equilateral $\displaystyle \triangle ABC$ is inscribed in a circle with centre O Then the measure of $\displaystyle \angle BOC$ is

  1. $\displaystyle 100^{\circ}$
  2. $\displaystyle 110^{\circ}$
  3. $\displaystyle 120^{\circ}$
  4. $\displaystyle 130^{\circ}$
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C Correct answer
Explanation

In an equilateral triangle inscribed in a circle, the angle subtended by a side at the center is 360 / 3 = 120 degrees.

AI explanation

In an equilateral triangle, each angle is 60 degrees, so the inscribed angle BAC is 60 degrees. By the Inscribed Angle Theorem, the central angle BOC is twice the inscribed angle subtending the same arc BC. Therefore, angle BOC equals 2 multiplied by 60 degrees, which gives 120 degrees.

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