Look at triangles ACB and HGF. Which equation must be true if and only if the figures are similar?
The answer choices are in the picture below and the question is there if you want to look at it there.

ALSO, it would really help me if you would give me a brief explanation of why you chose that answer. How did you solve it? This will really help me understand why its the correct answer.

Choice A isn't particularly useful because while it is a true statement, it doesn't help tie together the two triangles. It only helps us find angle A. It doesn't help is determine any connection to the other triangle. So we can rule choice A out.

Choice C is a similar story, but for the other triangle. So we can rule choice C out.

Choice B is a false statement because 180-(41+58) simplifies to 81; while 180-(41+75) simplifies to 64. This means the equation 180-(41+58) = 180-(41+75) simplifies to 81 = 64, which is false. We can rule choice B out.

The only thing left is choice D. If angle H was the measure of 180-(41+58) = 81, then we could conclude the triangles are similar. Recall that similar triangles have corresponding congruent angles. In the first triangle, the missing angle is A = 180-(41+58) = 81. If we can show that angle H is 81, then this forms one pair of congruent angles. The other pair would be angle F = angle B = 41. All we need at minimum are two pairs of congruent corresponding angles to prove the triangles similar. The theorem we would use is the AA (angle angle) Similarity Theorem.

So this is why choice D is the answer despite the fact that angle H in the diagram is shown to be 75. We would need to rewrite that angle in order to get the triangles to be similar. Currently the diagram shows two triangles that are not similar.