Question

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.

Answer 1

The measure of angle BEC in the parallelogram BCDE is 80 degrees.

Step-by-step explanation:

To find the measure of angle BEC in the parallelogram BCDE, we can use the properties of parallelograms and the given angle measures. Since opposite angles in a parallelogram are congruent, we know that angle BCD is also 60 degrees. Similarly, angle CBE is congruent to angle CED, so it is also 40 degrees. Therefore, angle BEC can be found by subtracting the given angle measures from 180 degrees:

angle BEC = 180° - angle BCD - angle CBE

angle BEC = 180° - 60° - 40°

angle BEC = 80°

Answer 2

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°