Geometry - Angle in Square and Equilateral Triangle

CAT 1996 Slot 1 · Quantitative Ability · Medium · QA

This is a medium Quantitative Ability question from the CAT 1996 Slot 1 paper. It tests QA. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

If $ABCD$ is a square and $BCE$ is an equilateral triangle constructed externally on side $BC$, what is the measure of $\angle DEC$?

1. A.

   $15^\circ$

2. B.

   $30^\circ$

3. C.

   $20^\circ$

4. D.

   $45^\circ$

Answer & explanation hiddenTry it firstShow answer

Answer

A

Explanation

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