1. **State the problem:** We need to find an angle $x$ such that the sum of its complementary and supplementary angles is 200 degrees. 2. **Recall definitions:** - Complementary angles sum to 90 degrees, so the complement of $x$ is $90 - x$. - Supplementary angles sum to 180 degrees, so the supplement of $x$ is $180 - x$. 3. **Set up the equation:** $$ (90 - x) + (180 - x) = 200 $$ 4. **Simplify the equation:** $$ 90 - x + 180 - x = 200 $$ $$ 270 - 2x = 200 $$ 5. **Solve for $x$:** $$ 270 - 2x = 200 $$ $$ -2x = 200 - 270 $$ $$ -2x = -70 $$ $$ x = \frac{-70}{-2} = 35 $$ 6. **Answer:** The angle is 35 degrees.