CAT 1996 | Question: 136

Question

If ABCD is a square and BCE is an equilateral triangle, what is the measure of the angle DEC?

• A. $15 ^{\circ}$
• B. $30 ^{\circ}$
• C. $0 ^{\circ}$ 
• D. $45 ^{\circ}$

Answer 1

In Square ABCD all sides are equal =d

In Equilateral Triangle BEC all sides are equal =d 

ABCD is a square and BCE is an equilateral triangle.

The angle DCE = 90 + 60 or 150 degrees.

Since BCE is an equilateral triangle, CE = CB = CD, so DEC is an isosceles triangle.

So angle DEC = angle EDC = x degrees

So    x+x+150=180

   x = (180 - 150)/2 = 30/2 = 15 degrees.

Option A is the Correct Answer.