First, let's finish filling in some information. If angle AED is 70, then angle BEC must also be 70. Since their sum is 140, the leftover degrees must add up to 220. Since angles AEB and DEC are equal, that means they are each 110 degrees. Angles EDC and ECD must also be equal, so they are both (180 - 110)/2 or 35 degrees. Since ADE and EDC are complimentary, angle ADE must be 55 degrees. Angle EAD is also 55 degrees. Now that we've finished that, we can begin solving for AE.
Seperate this into two triangles, bisected by line segment AC. The angles for this triangle are EAD (55 degrees), DCE (35 degrees), and ADC (90 degrees). If DC is 15, we can solve for AC by taking the 15/cos(35). AE is one half of that, so it must be B.
14. We already determined this was D.
15. We already determined this was C.
16. This one must be 90 degrees.