Square with external equilateral on a side – Find ∠BEC: ABCD is a square; on side CD an equilateral triangle CDE is constructed externally. Find the measure of ∠BEC.

Introduction / Context:Coordinate geometry offers a clean solution. Place A(0,0), B(1,0), C(1,1), D(0,1). Build equilateral CDE outward on CD; the third vertex E lies at (1/2, 1 + √3/2). Compute ∠BEC.

Concept / Approach:Use vectors EB and EC and the dot product formula cos θ = (EB · EC) / (|EB||EC|).

Step-by-Step Solution (Sketch):

Verification / Alternative check:Geometric angle-chasing using 30°–60°–90° relations on the equilateral triangle with square geometry also yields 15°.

Final Answer:15