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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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