In the given figure, AB is parallel to CD. Angle BAE = 72 degrees and angle BEA = 65 degrees. What is the value (in degrees) of angle ECD?
Show answer & explanation
Correct answer: A
Explanation
Given:
AB ∥ CD
∠BAE = 72°
∠BEA = 65°
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 − (72 + 65) = 43°
∠CED = ∠BEA = 65°
AB ∥ CD ⇒ ∠CDE = ∠ABE = 43°
Now, in triangle ECD:
∠ECD + 65 + 43 = 180
∠ECD = 180 − 108 = 72°