1. **Problem:** Two supplementary angles are in a ratio of 5:3. Find the measure of the larger angle. 2. **Formula and rules:** Supplementary angles add up to 180 degrees. If the angles are in ratio 5:3, let the angles be $5x$ and $3x$. 3. **Work:** $$5x + 3x = 180$$ $$8x = 180$$ $$x = \frac{180}{8} = 22.5$$ 4. **Find 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 and rules:** Complementary angles add up to 90 degrees. Let the angles be $8y$ and $7y$. 3. **Work:** $$8y + 7y = 90$$ $$15y = 90$$ $$y = \frac{90}{15} = 6$$ 4. **Find smaller angle:** $$7y = 7 \times 6 = 42$$ --- 1. **Problem:** Find the complement of 63. 2. **Formula:** Complement of angle $\theta$ is $90 - \theta$. 3. **Work:** $$90 - 63 = 27$$ --- 1. **Problem:** Find the supplement of 63. 2. **Formula:** Supplement of angle $\theta$ is $180 - \theta$. 3. **Work:** $$180 - 63 = 117$$ --- 1. **Problem:** What is 8% of 400? 2. **Formula:** Percent of a number is $\frac{\text{percent}}{100} \times \text{number}$. 3. **Work:** $$\frac{8}{100} \times 400 = 32$$ --- 1. **Problem:** 26 is what percent of 65? 2. **Formula:** Percent = $\frac{\text{part}}{\text{whole}} \times 100$. 3. **Work:** $$\frac{26}{65} \times 100 = 40$$ --- **Final answers:** 1. Larger supplementary angle = 112.5 degrees 2. Smaller complementary angle = 42 degrees 3. Complement of 63 = 27 degrees 4. Supplement of 63 = 117 degrees 5. 8% of 400 = 32 6. 26 is 40% of 65