Bcde is a parallelogram. what is the measure of ∠bec? enter your answer in the box. ° a parallelogram b c d e. side e d is the base. the pairs of opposite sides are parallel. diagonal e c divides the parallelogram into triangles c d e and b c e. angle b is labeled 60 degrees and angle c e d is labeled 40 degrees.

Solution:

In Parallelogram B CDE

BC= DE, BC ║DE

CD = BE , CD ║BE

Also, ∠B=∠D and ∠C=∠E →→In a parallelogram opposite sides are equal and parallel, as well as opposite angles are equal.Diagonals Bisect each other.

∠B= 60° , ∠C ED= 40°

CE is a transversal and BC║DE.

∠CED=∠BCE = 40° →→Alternate interior angles

In Δ BCE

∠B + ∠BCE + ∠BEC= 180°→→→Angle sum property of Triangle.

60° + 40° + ∠ B E C= 180°

100° + ∠BEC=180°

∠BEC= 180° -100°

∠BEC= 80°

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step-by-step explanation: