In the given figure, AB is parallel to CD. Angle BED = 130 degrees and angle CDE = 55 degrees. What is the value (in degrees) of angle ABE?
Show answer & explanation
Correct answer: D
Explanation
Given:
AB ∥ CD
∠BED = 130°
∠CDE = 55°
Alternate interior angles formed by parallel lines are equal.
Sum of angles:
AB ∥ CD ⇒ ∠BEF = ∠CDE = 55°
∠BED = 130° ⇒ ∠FEB = 130° − 55° = 75°
EF ∥ AB ⇒ ∠ABE = ∠FEB = 75°