1. **Problem:** Two supplementary angles are in a ratio of 5:3. Find the measure of the larger angle. 2. **Formula:** Supplementary angles add up to 180 degrees, so if the angles are $5x$ and $3x$, then: $$5x + 3x = 180$$ 3. **Solve for $x$:** $$8x = 180$$ $$x = \frac{180}{8}$$ $$x = 22.5$$ 4. **Find the larger angle:** $$5x = 5 \times 22.5 = 112.5$$ --- 1. **Problem:** Two complementary angles are in a ratio of 8:7. Find the measure of the smaller angle. 2. **Formula:** Complementary angles add up to 90 degrees, so if the angles are $8y$ and $7y$, then: $$8y + 7y = 90$$ 3. **Solve for $y$:** $$15y = 90$$ $$y = \frac{90}{15}$$ $$y = 6$$ 4. **Find the smaller angle:** $$7y = 7 \times 6 = 42$$ --- 1. **Problem:** Find the complement of 63. 2. **Formula:** Complement of an angle $a$ is $90 - a$. 3. **Calculate:** $$90 - 63 = 27$$ --- 1. **Problem:** Find the supplement of 63. 2. **Formula:** Supplement of an angle $a$ is $180 - a$. 3. **Calculate:** $$180 - 63 = 117$$ --- 1. **Problem:** What is 8% of 400? 2. **Formula:** Percent of a number is given by $\frac{percent}{100} \times number$. 3. **Calculate:** $$\frac{8}{100} \times 400 = 32$$ --- **Final answers:** - Larger supplementary angle: $112.5$ degrees - Smaller complementary angle: $42$ degrees - Complement of 63: $27$ degrees - Supplement of 63: $117$ degrees - 8% of 400: $32$