To find the angle measure of vertex C using the inverse tangent function, we typically need some side lengths of a right triangle that include vertex C. The inverse tangent function (arctan) is used when you have the lengths of the opposite side and the adjacent side.
The formula for finding the angle \( C \) is:
\[ C = \tan^{-1}\left(\frac{\text{opposite}}{\text{adjacent}}\right) \]
However, you have not provided specific lengths. If you have the lengths of the sides, please share those to compute the angle. If these angles (37°, 53°, 59°, or 39°) are from a multiple-choice problem and you have the ratios, I can help deduce the correct angle based on those ratios.
Please provide the necessary information to find the angle measure!