Answer:
<em>x = 13 deg</em>
Step-by-step explanation:
As shown in the picture, you have:
CF and CD are perpendicular
=> angle BCF = 90 deg
=> angle BCE + angle ECF = angle BCF = 90 deg
or angle BCE + 64 = 90
=> angle BCE = 90 - 64 = 26 deg
Point A, B, and C are collinear
=> (angle ABE) + angle CBE = 180 deg (1)
Otherwise, as the property of the sum of 3 angles in a triangle:
(angle BEC + angle BCE) + angle CBE = 180 deg (2)
From (1) and (2) you would have:
angle ABE = angle BEC + angle BCE
or
3x = 26 + x
<=> 3x - x = 26
<=> 2x = 26
<=> x = 26/2
<=> x = 13
=> angle BEC = x = 13 deg
=> angle ABE = 3x = 3(13) = 39 deg
Hope this helps!
