Final answer:
Without a specific diagram or context, we cannot accurately solve for x and the measure of angle PSR. Typically, these problems involve applying geometric properties of a median and trigonometric ratios or identities.
Step-by-step explanation:
The question is asking to solve for the variable x and the measure of angle PSR in a geometric figure where PS is a median. The information given suggests the need for an understanding of geometry, measurement, and trigonometric functions, possibly within the context of the median-median line or polar coordinates.
However, the question references multiple scenarios, and without a specific context or diagram, we cannot provide an accurate solution. In general, when solving for x within geometric figures, one would apply geometric postulates, properties of medians, and algebraic techniques.
The measure of angle PSR would typically be determined using trigonometric ratios (sine, cosine, tangent) if the lengths of the sides of the triangle are known, or by using the properties of the median if applicable.
The solution process could involve setting up equations based on the properties of the median (that it divides the opposite side of the triangle into two equal parts) and applying trigonometric identities or theorems like the Law of Sines or Cosines if the triangle is not right-angled. If specific numeric values and a diagram were given, one could use these values to solve for x and calculate the angle PSR.
The complete question is: PS is a median. Solve for x and measure of angle PSR. is: