Simple Geometry Problem, but

I don't understand what's going on here. It's the beginning of the book too. Maybe I missed something here.

http://i575.photobucket.com/albums/ss196…

Find Angle ADC if c = 45 degrees and d = 85 degrees. The answer is 130 degrees.

But then this part I don't understand...

Find Angle AEB if e = 60 degrees.

The answer is 120 degrees. But why?

ABD is a right triangle and we know that c = 45 so A must be 45 as well.
Since e = 60 and c = 45 then EBD is 180 - 45 - 60 =75

Since B = 90 and EBD is 75 the remainder ABE = 90-75 = 15
Since A = 45 and a = 15 then AEB is 180 - 15 - 45 = 120

Additional Details:
Since ABD = 90 and b = 42 then ABC = 90 + 42 = 132
Since e = 60 and c = 45 then EBD is 180 - 45 - 60 =75

Angle AEB is 120 degrees because it is supplementary to angle e, which is 60 degrees. If two angles are supplementary, they add up to 180 and create a straight line. 180-60=120 (angle AED - angle BED = angle AEB).

For the next set of problems, you need to use the basis that angle ABD is 90 degrees, because it is right. EBD must be 75 because 90-15=75 (angle a was 15 degrees). Since angle b is 42 degrees, ABD is 132 since 42+90=132

angle e+angle AEB=180( sum of angles on a straight line is 180)
as e=60
60+angleAEB=180
angle AEB=120
angle ABD=90(given in the figure)
angle ABD=angle a+ angle EBD

90=15+angle EBD
angle EBD=75

angle ABC=angle ABD+angle b
angle ABC=90+42=132

AED is a straight line, so ∠AEB + ∠e = 180°.
∠AEB = 180 - ∠e = 120°
:::::
∠EBD = 180 - ∠e - ∠c = 75°
∠ABC = 90 + ∠b = 132°

Line AD is a so called straight angle and must equal 180, 180 - 60 = 120.

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