Answer:
m∠AEC = 139°
Step-by-step explanation:
To make the equations easier to write, let's say all measures are in degrees, and define ...
p = m∠AEB = 11x -12
q = m∠CED = m∠CEB = 4x +1
Then ...
p + 2q = 180
(11x -12) + 2(4x +1) = 180
19x -10 = 180 . . . . . . . . . . . . collect terms
19x = 190 . . . . . . . . add 10
x = 10 . . . . . . . . . . . divide by 19
p = 11x -12 = 110 -12 = 98
q = 40 +1 = 41
The angle of interest is ...
m∠AEC = p +q = 98 +41
m∠AEC = 139 . . . . degrees
