In a square ABCD, E is a point inside the square such that ΔDEC is an equilateral triangle. If E is joined to vertices A and B of the square, what is the degree measure of ∠AEB?

Explanation

Concept: The sum of all the angles of the triangle = 180∘ Calculation: Let the side of the square ABCD = a As per the question, ΔDEC is an equilateral triangle. ⇒ ∠DEC = ∠ECD = ∠CDE = 60∘ ------ eq (1) ⇒ DC = DE = CE = AD = CB = AB = a ------ eq (2) ⇒ ∠ADE = 90∘ - 60∘ = 30∘ (all the angles of the square = 90) Now, AD = DE, as per eq (2) So, ΔADE is an isosceles triangle. ⇒ ∠DAE = ∠DEA = (180 - 30)/2 = 75∘ ⇒ ∠DAE = 75∘ ⇒ Similarly, ∠CBE = 75∘ ∘ ⇒ ∠EAB = ∠EBA = 90∘ - 75∘ = 15 ∴ ∠AEB = 180∘ - (15∘ + 15∘ ) = 150∘ Hence, the correct answer is Option 2).