20pts. Find the measure of ∠BEC. A) 10° B) 60° C) 80° D) 100°

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°