In the diagram below, AB||DC, the bisectors of < BAC and < ACD meet at E. Find the value of < AEC
Attached Figure / Diagram
A
45°
B
60°
C
30°
D
90°
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
∠BAC = 90°
∠ACD = 90° if AE and CE are the bisectors of ∠BAC and ∠ACD respectively ∠BAE = 45°; ∠DCE = 45°
∴ ∠EAC = ∠ECA = 45°
But ∠EAC + ∠ACE + ∠AEC = 180° (angle in a △)
∴ 45° + 45° + ∠AEC = 180°
∠AEC = 180° - 90°
∠AEC = 90°
Source: WAEC / JAMB / NECO Classroom Archive (Record #75907)