Need with geometry (identifying angles with terminology)

Wow !  I don't think I've ever seen a problem that was filled with so much stuff that's only there to distract and confuse you.

If you can, get rid of everything in that drawing except the two lines that intersect at C.  Those other 3 lines, and the 10 letter labels on them, have nothing to do with this question, and no effect on the answer.

When you clear out all the clutter, and just look at the little  neighborhood around ' C ', you'll notice that the two angles they're asking about are both formed by the same two intersecting lines, their vertexes are the same point, but they don't share any side.  They're called "vertical angles", even though they're not necessarily vertical.

The letter ' X ' is a beautiful example of vertical angles.  It has 2 pairs of them. The upper and lower angles are a pair of vertical angles, and the left and right are another pair.  Each pair is formed by two intersecting lines, their vertexes are both at the same point, but they don't share any sides.

Now here's the big news: Vertical angles are equal.

That's a law of geometry. Memorize it.  It's the answer to this question, and now you have a new tool in your math toolbox that you'll be able to use for many years.

486in is correct

step-by-step explanation:

6 adults and 9 children went.

a + c = 15

12a + 9c = 153

12(6) + 9(9) = 153

72 + 81 = 153