More math:
https://snipboard.io/viE326.jpg

Question

More math: 
https://snipboard.io/viE326.jpg

Extrinix · Answer

Seeing that $\overline{AD}$ is parallel to $\overline{BC}$, we'll look for a $180^\circ$ now, to find $\angle A$ we need to find out which angles are similar, $\angle A$ is similar to $\angle D$ and $\angle B$ is similar to $\angle C$, now the only choice for $\angle A$ is this: $\angle A + \angle B = 180$ but $(x+16)+(x) = 180$ is not an option, so look for the similar angle, $\angle C$ now we can create the equation for $\angle A + \angle C = 180$ this would be, $(x+16)+(6x-4) = 180$ so, answer choice 1 would be your answer.

darkknight · Answer

You got the correct answer but I would like to disagree with your reasoning, We can not assume that the lines are parallel, a property is that opposite angles of a quadrilateral are supplementary which then you can use that to prove all that above. But AD does not have to be parallel to BC

darkknight · Answer

Unless specifically stated in a problem you can't make an assumption like that, so that is the correct reasoning, angles opposite in a quadrilateral inscribed in a circle are supplementary which you then use to prove

extrinix wrote:

now the only choice for $\angle A$ is this: now we can create the equation for $\angle A + \angle C = 180$ this would be, $(x+16)+(6x-4) = 180$ so, answer choice 1 would be your answer.