Final answer:
The measure of angle Y in isosceles triangle WXY, where sides YW and XY are congruent and m∠X is 38°, should theoretically be 104°. There might be a typo as this answer is not given in the options, with 114° (Option C) being the closest. It's important to recheck the provided information for any errors.
Step-by-step explanation:
We are given a triangle WXY with sides YW and XY being congruent. This information suggests that ∃WXY is an isosceles triangle with two equal sides (YW ≅ XY). Since the angles opposite to equal sides in an isosceles triangle are also equal, if m∠X is given as 38°, then m∠W would be the same - 38°. To find m∠Y, we will use the fact that the sum of angles in any triangle equals 180°:
m∠Y + m∠W + m∠X = 180°
m∠Y + 38° + 38° = 180°
m∠Y + 76° = 180°
m∠Y = 180° - 76°
m∠Y = 104°
Therefore, the measure of angle Y, m∠Y, is 104°. However, since this option is not available in the choices provided, it could be a typo or a misrepresentation of the options (A, B, C, D). The closest correct answer from the options listed would be Option C with 114° which might be due to a typographical error in the problem statement or answers listed.