Final answer:
Given m∠2 = 63º and assuming the angles are vertical or supplementary due to intersecting lines, m∠1 and m∠4 would also be 63º, and m∠3 would be 117º, corresponding to option A.
Step-by-step explanation:
To find m∠1, m∠3, and m∠4 given m∠2 = 63º, we need additional geometric details such as whether the angles are supplementary, complementary, vertical, or correspond to some known geometric shape or configuration. Unfortunately, the question lacks those details. Nevertheless, a possible situation where this calculation could apply is when dealing with angles formed by two intersecting lines. In that case, angles across from each other (vertical angles) are equal, so if m∠2 is given as 63º, m∠4 would also be 63º. Similarly, m∠1 would be equal to m∠2 since they are also vertical angles. Angles m∠2 and m∠3 would then be supplementary if they are adjacent angles formed by the intersecting lines, so m∠3 would be 180º - 63º = 117º.
Therefore, the correct answers, assuming the angles are formed by two intersecting lines, would be m∠1 = 63º, m∠3 = 117º, and m∠4 = 63º, which corresponds to option A.