Final answer:
Complementary angles sum up to 90°, so if angle B is 55°, angle A must be 35°. The statement 'sin(B) = sin(A)' is incorrect because the sine values of different angles are not equal, but it is true that sin(A) equals cos(B) and sin(B) equals cos(A) for complementary angles.
Step-by-step explanation:
If m∠A and m∠B are complementary angles and m∠B is a 55° angle, it means that m∠A is 35° since complementary angles sum up to 90°. Now considering the original statement, sin(B) = sin(A), which is not generally true for two non-identical angles, let's apply the definition of sin to these angles. Since sin(55°) and sin(35°) are values for different angles, they are not equal.
However, there's something interesting to note here: the sine of an angle is equal to the cosine of its complement in a right triangle (due to the co-function identity), so sin(55°) = cos(35°) and sin(35°) = cos(55°). In this case, to compare the sines of A and B correctly, we would rather compare sin(A) with cosine of B and vice versa. If m∠B were given as 55°, then sin(A) would equal cos(B) not sin(B).