Explanation:

Let’s break it down:

- ?A : ?B : ?C = 3 : 3 : 4. That’s 3x, 3x, 4x. All angles in a triangle add up to 180°, so

3x + 3x + 4x = 180 ? 10x = 180 ? x = 18

So: ?A = ?B = 54°, ?C = 72°

- Now, a line parallel to BC cuts AB at P and AC at Q. PQ is parallel to BC, so triangle APQ is similar to triangle ABC.

- In these similar triangles, corresponding angles at A are equal. At P and Q, let’s label angles:

At Q: angle between AQ and PQ = angle QAP = a

At P: angle between PA and PQ = angle QPA = ß

- Since PQ is parallel to BC (let’s picture that), by similarity and alternate interior angles:

?AQP = ?B (so 54°)

?APQ = ?C (so 72°)

- So ?AQP - ?APQ = 54° - 72° = -18°

- Taking positive difference (as options are all positive): 18°

Here’s the answer:

- Option 1: 12 [nope, too low]

- Option 2: 18 This is right

- Option 3: 24 [doesn’t match]

- Option 4: 36 [way too high]

Option 2 is correct.