If ABCD is a square and BCE is an equilateral triangle, what is the measure of ∠DEC?
Explanation:
Since ΔBCE is an equilateral triangle, CE = BC = BE. And since ABCD is a square, BC = CD. Hence, CD = CE. So in ΔCDE, we have CD = CE. Hence, ∠EDC = ∠CED. Now ∠BCE = 60° (since equilateral triangle) and ∠BCD = 90° (since square). Hence, ∠DCE = ∠DCB + ∠BCE = (60 + 90) = 150°. So in ΔDCE, ∠EDC + ∠CED = 30° (since three angles of a triangle add up to 180°). Hence, we have ∠DEC = ∠EDC = 15°.
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