Final answer:
Without additional information about the figure or the relationship between angles TXS and SXU, it's impossible to determine the measure of ∠SXU. In general, knowing the sum of angles in a triangle is 180 degrees or that supplementary angles add up to 180 degrees could provide a potential solution in some contexts.
Step-by-step explanation:
If ∠TXS=61°, then to determine ∠SXU, more information about the figure or the relationship between angles TXS and SXU is needed. Since we have no additional information or context, such as whether TXS and SXU are complementary, supplementary, or form part of a particular geometric shape like a triangle or a polygon, we cannot give a specific answer to what the measure of ∠SXU is.
However, we can provide a general approach to these types of problems. In geometry, the sum of the angles in a triangle is 180 degrees. If angles TXS and SXU are part of the same triangle, you would subtract the known angle from 180 to find the sum of the other two angles. If ∠SXU is supplementary to ∠TXS (they form a straight line), then ∠SXU would be 180 degrees minus 61 degrees, which equals 119 degrees. Without specific information about the figure or the relationship of the angles, we apply general rules to estimate the measure.
The reference to trigonometry provided in the question prompt seems not directly related to finding ∠SXU, but is a useful reminder that trigonometry is a tool often used to solve for unknown sides and angles in right triangles.