1. **State the problem:** We have two intersecting lines forming four angles. One angle is given as 50° (bottom-left). We need to find the measures of the missing angles $b$ (top-right) and $c$ (bottom-right). 2. **Recall the rules:** - Vertically opposite angles are equal. - Adjacent angles on a straight line sum to 180°. 3. **Identify angles:** - The angle opposite 50° (top-right) is $b$, so $b = 50°$ by vertical angles. 4. **Find angle $c$:** - Angles $50°$ and $c$ are adjacent and form a straight line, so their sum is 180°. 5. **Calculate $c$:** $$ 50° + c = 180° $$ $$ c = 180° - 50° $$ $$ c = 130° $$ **Final answers:** - $b = 50°$ - $c = 130°$