Final Answer:
The value of m is m=32 because the measures of ∠ X and ∠Y are equal. Thus, the correct answer is option C.
Step-by-step explanation:
When two angles are said to be equal, it implies that their measures are identical. In this context, the equality of measures for ∠X and ∠ Y means that m is equal to the measure of both angles. Therefore, m must be 32 degrees, as stated in option C.
To elaborate further, let's assume ∠X and ∠Y both have a measure of m. The equality condition can be expressed as m(∠X) = m(∠Y). If m is 32 degrees, then m(∠X) = m(∠Y) = 32. This satisfies the given condition of equal measures.
Conclusively, by selecting option C, which corresponds to m=32, we ensure that the measures of ∠X and ∠Y are indeed equal. This demonstrates the fundamental concept in geometry that when two angles are stated to be equal, the numerical measure of each angle is the same, and in this case, that measure is 32 degrees.