I'm having a hard time finding that m

Question

I'm having a hard time finding that m<E = 25 (the correct answer). Triangle AEB is NOT isosceles

anonymous · Answer

See attached

asnaseer · Answer

I have filled-in the angles that can be worked out directly and labelled the rest as follows:
|dw:1325721373971:dw|
m<BCA = m<CBE + m<CEB (external angle of a triangle)
        75 = alpha + beta                     <--- (1)
m<BCA + m<BCD + m<DCE = 180 (angle on a straight line)
75 + 180 - 2alpha + beta = 180
       75 = 2alpha - beta                     <--- (2)

2*(1) - (2) gives:
75 = 3beta
25 = beta