1. **Problem Statement:** We are given a protractor with rays labeled OU (0°), OT (~20°), OS (~50°), OR (90°), OQ (~140°), and OP (180°). We need to find the measures of the angles: (i) $\angle POQ$, (ii) $\angle POT$, (iii) $\angle POR$, (iv) $\angle POU$, and (v) $\angle POS$. 2. **Formula and Rules:** The measure of an angle formed by two rays is the absolute difference between their degree measures on the protractor. 3. **Calculations:** (i) $m \angle POQ = |180^\circ - 140^\circ| = 40^\circ$ (ii) $m \angle POT = |180^\circ - 20^\circ| = 160^\circ$ (iii) $m \angle POR = |180^\circ - 90^\circ| = 90^\circ$ (iv) $m \angle POU = |180^\circ - 0^\circ| = 180^\circ$ (v) $m \angle POS = |180^\circ - 50^\circ| = 130^\circ$ 4. **Explanation:** To find each angle, subtract the smaller ray degree from the larger ray degree because the protractor measures angles from 0 to 180 degrees. The absolute value ensures the angle measure is positive. **Final answers:** (i) 40° (ii) 160° (iii) 90° (iv) 180° (v) 130°