Line BD bisects angle ADC. The measure of angle ADB=4a and the measure of angle CDB=(a+66). What is m<ADC?

So if you draw the picture you see that angle ADB needs to equal angle CDB because the line bisects which means that it cuts ADC in half. If one angle is 4a and the other a+66 then you set those two equations = to equal to each other and solve for a. a is 22. Then you plug that into either of your original equations to find out what either angle ADB or CDB is and it is 88. Multiply this times 2 which is 176. It makes more sense if you draw the picture.