Final answer:
Without additional information, such as the length of side BC or the measure of angle ∠C, we can't determine the measure of ∠A. We can only express ∠A as 180 degrees minus ∠B and ∠C.
Step-by-step explanation:
If we are given the lengths of two sides of a triangle, and the measure of the angle between those sides, we can find the measure of another angle using the Law of Sines. However, the information provided here does not involve any ratio that would typically be used in the Law of Sines, as we are not given the length of the side opposite to the given angle. But if we assume that ABC is a triangle, we can use the fact that the sum of the angles in a triangle is always 180 degrees. Since the given angle ∠B is 58 degrees, we can denote ∠A as the angle we want to find and ∠C as the third angle.
To find ∠A, we need the following equation: ∠A + ∠B + ∠C = 180 degrees. Because we are not given ∠C or any other sides' lengths, we cannot solve for ∠A without additional information. Usually, in such cases, more data regarding the sides or angles is necessary, such as the length of side BC or the measure of angle ∠C.
With the given information alone, we can only express ∠A as 180 degrees - ∠B - ∠C. To provide a specific measure for ∠A, more data about the triangle is needed. Therefore, with only what has been provided, ∠A remains indeterminate.