In the adjoining figure ABCD is a square and BCE is an equilateral triangle on the side BC of the square. Find the ∠DEC.

GIVEN:

BCE is an equilateral triangle on the side BC of the square ABCD.

CONCEPT:

Each angle of an equilateral triangle is 60°

Each angle of square is 90°

FORMULA USED:

Sum of all the angles of a triangle = 180°

CALCULATION:

Since BCE is an equilateral triangle:

∠BCE = 60°

Now,

∠DCE = 90° + 60° = 150°

DC = CE = x (Suppose)

So,

∠DEC = ∠CDE = x° (Angle opposite to the equal sides are equal)

⇒ 2x° + 150° = 180

⇒ x° = 15°

∴ ∠DEC is 15°.