Question:
If ABCD is a square and BCE is an equilateral triangle, what is the measure of \( \angle DEC \)?
If ABCD is a square and BCE is an equilateral triangle, what is the measure of \( \angle DEC \)?
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Use known angle properties of squares and equilateral triangles to calculate unknown angles.
Updated On: Jul 24, 2025
- 15°
- 30°
- 20°
- 45°
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The Correct Option is B
Solution and Explanation
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°.
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°.
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