<h2>Explanation:</h2><h2></h2>
The figure to this problem is attached below. We know that angles ∠AEG and ∠GEC are supplementary, so:
∠AEG + ∠GEC = 180°
∠AEG = 8x°
∠GEC = (4x + 60)°
8x° + (4x + 60)° = 180°
(12x + 60)° = 180°
12x + 60 = 180
12x = 180 - 60
12x = 120
x = 10
∠AEG and ∠BEC are vertical angles, so they are congruent:
∠BEC = 8x°
∠BEC = 8(10)°
∠BEC = 80°