Geometry - Angle in Square and Equilateral Triangle

CAT 1996 Slot 1 · QA · Medium · QA

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If ABCDABCD is a square and BCEBCE is an equilateral triangle constructed externally on side BCBC, what is the measure of ∠DEC\angle DEC?

  1. A.

    15∘15^\circ

  2. B.

    30∘30^\circ

  3. C.

    20∘20^\circ

  4. D.

    45∘45^\circ

Answer

A

Explanation

In △CDE\triangle CDE, CD=CE=BCCD = CE = BC. ∠DCE=90∘+60∘=150∘\angle DCE = 90^\circ + 60^\circ = 150^\circ. Since CD=CECD = CE, ∠DEC=∠EDC=180∘−150∘2=15∘\angle DEC = \angle EDC = \frac{180^\circ - 150^\circ}{2} = 15^\circ.

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