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

1. $15 ^{\circ}$
2. $30 ^{\circ}$
3. $0 ^{\circ}$
4. $45 ^{\circ}$
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+1 vote

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.

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