The question is asking for ABC in terms of the other variables, we should disclude q as ABC = q already, and try to represent ABC with the other variables.

Connect BD and observe the two created angles can be represented by \(180 - r\). Next, observe the biggest triangle (which was just created) and we have the relation p + q + (180 - r) + s = 180. We want ABC = q = .... so we have:

\(\angle ABC = q = 180 - p - s - (180 - r) = -p - s + r = r - (p + s)\).

Ans: A
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Let's create a line from point A to point C, dividing the figure into 2 triangles: ABC and ACD. Since the sum of angles of each angle must be 180, the sum of all internal angles of ABCD must equal to 360. The sum of angles ACB and ACD is equal to 360-angle BCD. angle BAC + angle DAC =angle BAD. ------> p+q+360-r+s=360 ----> r=p+q+s -----> q=r-(p+s) A)

180 = p + q + s + x + y <--- x + y are the two unknown angles in the bottom triangle that can be formed by connecting ∠A and ∠C

180 = p + q + s + (180 - r) <--- x + y is equivalent to 180 - r

q = r - p - s = r - (p + s)

Answer is A.
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