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°