Question

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

• A. 15°
• B. 30°
• C. 20°
• D. 45°

Hint:

Use known angle properties of squares and equilateral triangles to calculate unknown angles.

Answer 1

The Correct Option is B

We are given that \( ABCD \) is a square, so all its angles are 90°. Additionally, \( BCE \) is an equilateral triangle, meaning all its angles are 60°. We are tasked with finding \( \angle DEC \). Step 1: The angle \( \angle EBC \) in the equilateral triangle \( BCE \) is 60°.
Step 2: The angle \( \angle DBC \) in the square is 90°. Since \( \angle DBC = \angle EBC + \angle DEC \), we have: \[ 90° = 60° + \angle DEC \] \[ \angle DEC = 30° \] Thus, the answer is b. 30°.