1. **Problem statement:** Find the measures of arcs and angles in a circle where given angles are 87° and 135°, and unknowns are $x$ and $y$. 2. **Relevant formulas and rules:** - The sum of angles around a point is 360°. - Angles subtended by the same arc are equal. - The measure of an arc intercepted by an angle is related to the angle by circle theorems. 3. **Step-by-step solution:** - Given angles are 87° and 135°, and unknowns $x$ and $y$ are arcs or angles related to these. - Since the angles 87° and 135° are adjacent or related, the sum $x + y$ can be found by subtracting from 360° or using supplementary angle rules. - If $x$ and $y$ are arcs intercepted by these angles, then $x = 87°$ and $y = 135°$ or vice versa depending on the figure. 4. **Final answer:** - $x = 87°$ - $y = 135°$