Please help me with this problem, thank you.

The answer is just 117.

Every straight line is 180 degrees, meaning that the angle of ∠ABE and ∠CBE must add up to 180. You can say that ∠ABE + ∠CBE = 180. If you rearrange, you can see that ∠ABE = 180 - ∠CBE. Since ∠CBE is given as 63, all you need to do is subtract this from 180 to get 117.

Hope this helps!

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.