Answer:
277°
Step-by-step explanation:
The measure of arc AEG = AB + BE + EF + FG
The central angle is congruent to the arc that subtends it
∠ ECB = 180° - 44° = 136° ( adjacent angles )
∠ECF = ∠ ACB = 44° ( vertical angles ), thus
AEG = 44° + 136° + 44° + 53° = 277°
