Question : Inside a square ABCD, $\triangle$BEC is an equilateral triangle. If CE and BD intersect at O, then $\angle$BOC is equal to:
Option 1: 60°
Option 2: 75°
Option 3: 90°
Option 4: 120°
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Correct Answer: 75°
Solution :
Given: Inside a square ABCD, $\triangle$BEC is an equilateral triangle.
In $\triangle$BOC,
$\angle$BCO = 60° (angle of an equilateral triangle)
$\angle$OBC = $\frac{90°}{2}$ = 45° (as the diagonal of a square bisects its angle into two equal parts)
So, $\angle$BOC = 180° – (60° + 45°) = 75°
Hence, the correct answer is 75°.
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