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ABCD is a square and Q is a point in its interior such that ΔQAB is equilateral. The measure of ∠QCB is: -

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Question

ABCD is a square and Q is a point in its interior such that ΔQAB is equilateral. The measure of ∠QCB is:

Options

  • 60°

  • 45°

  • 75°

  • 30°

MCQ

Solution

75°

Explanation:


ΔQAB is an equilateral triangle

∠QAB = ∠QBA = ∠AQB = 60°

AB = AQ = BQ

In ΔQBC, QB = BC .....(Side of square)

∠BQC = ∠BCQ

∠ABC = 90° and ∠ABQ = 60°

∴ ∠QBC = (90 – 60)° = 30°

∴ ∠BCQ = `((180 - 30))/2` = 75°

∠BCQ = ∠QCB = 75°

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Geometry (Entrance Exam)
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