Let's begin by understanding the problem. We have a geometric figure where points Q, R, S, and T all lie on line segment PV. Line segment RU intersects line segment SX at point W. We are given several angle measurements: angle SQX is 48 degrees, angle SXQ is 86 degrees, angle SWU is 85 degrees, and angle VTU is 162 degrees. Our goal is to find the measure of angle TUR.Let's start by analyzing triangle QSX. We know that angle SQX is 48 degrees and angle SXQ is 86 degrees. Using the triangle angle sum property, which states that the sum of all angles in a triangle equals 180 degrees, we can find angle QSX. We calculate: 180 minus 48 minus 86, which equals 46 degrees. So angle QSX is 46 degrees.