In the given figure, AB is parallel to CD. Angle BAE = 55 degrees and angle BEA = 45 degrees. What is the value (in degrees) of angle ECD?
Show answer & explanation
Correct answer: B
Explanation
Given:
AB ∥ CD
∠BAE = 55°
∠BEA = 45°
The sum of the angles of a triangle = 180°
Vertically opposite angles are equal
Alternate interior angles formed by parallel lines are equal
In triangle ABE,
∠ABE = 180 − (55 + 45) = 80°
∠CED = ∠BEA = 45°
AB ∥ CD ⇒ ∠CDE = ∠ABE = 80°
Now, in triangle ECD,
∠ECD + 45 + 80 = 180
∠ECD = 180 − 125 = 55°