Final answer:
m∠2 is equal to m∠27 because they are corresponding angles, and m∠4 is supplementary to m∠27 because they are alternate interior angles. Therefore, m∠2 = 63°, and m∠4 = 117°.
Step-by-step explanation:
When two parallel lines are cut by a transversal, corresponding angles are equal, and alternate interior angles are supplementary. Since m∠27 is given as 63° and it corresponds to m∠2 on the parallel lines, m∠2 must also be 63°. Additionally, m∠4 is an alternate interior angle to m∠27, so m∠4 would be supplementary to it, which means m∠4 = 180° - 63° = 117°. Therefore, the answer is A) m∠2 = 63°, m∠4 = 117°.