Question

In the given parallelogram, BE and CE are angle bisectors. If m∠A = 70°, find m∠BEC.

Answer 1

Answer:

∠BEC=90°

Step-by-step explanation:

∠A=∠BCD and ∠ABC=∠D because opposite angles in a parallelogram are equal.

∠A=∠BCD=70

All angles in a quadrilateral add to 360:

∠A+∠ABC+∠BCD+∠D=360

∠ABC+∠D=360-140=220

∠ABC=∠D=110

Since ∠ABC=∠ABE+∠EBC, and ∠ABE=∠EBC (because BE is an angle bisector), ∠EBC=55.

Since ∠BCD=∠BCE+∠ECD, and ∠BCE=∠ECD (because CE is angle bisector), ∠BCE=35.

All angles in a triangle add to 180:

∠BCE+∠EBC+∠BEC=180

35+55+∠BEC=180

∠BEC=180-90

∠BEC=90°