1. Problem 13: Find the measure of the angle at point V formed by a tangent and a chord intercepting an arc of 160°. 2. Formula: The angle formed by a tangent and a chord is half the measure of the intercepted arc. $$\text{Angle} = \frac{1}{2} \times \text{Intercepted Arc}$$ 3. Calculation: $$\text{Angle} = \frac{1}{2} \times 160 = 80^\circ$$ 4. Explanation: The angle between a tangent and a chord is always half the intercepted arc's measure. Here, the arc is 160°, so the angle is 80°. 5. Problem 14: Find the measure of the intercepted arc when the angle formed by a tangent and a chord is 58°. 6. Using the same formula: $$58 = \frac{1}{2} \times \text{Arc}$$ 7. Multiply both sides by 2: $$2 \times 58 = \cancel{2} \times \frac{1}{\cancel{2}} \times \text{Arc} \Rightarrow 116 = \text{Arc}$$ 8. So, the intercepted arc is 116°. 9. Problem 15: Given angle 35° and arc expression $24x + 2$, find $x$. 10. Using the formula: $$35 = \frac{1}{2} (24x + 2)$$ 11. Multiply both sides by 2: $$2 \times 35 = \cancel{2} \times \frac{1}{\cancel{2}} (24x + 2) \Rightarrow 70 = 24x + 2$$ 12. Subtract 2 from both sides: $$70 - 2 = 24x \Rightarrow 68 = 24x$$ 13. Divide both sides by 24: $$\frac{68}{\cancel{24}} = \frac{24x}{\cancel{24}} \Rightarrow \frac{68}{24} = x$$ 14. Simplify fraction: $$x = \frac{17}{6} \approx 2.83$$ 15. Problem 16: Given arc 200° and angle expression $21x - 4$, find $x$. 16. Using the formula: $$21x - 4 = \frac{1}{2} \times 200$$ 17. Calculate right side: $$21x - 4 = 100$$ 18. Add 4 to both sides: $$21x - 4 + 4 = 100 + 4 \Rightarrow 21x = 104$$ 19. Divide both sides by 21: $$\frac{21x}{\cancel{21}} = \frac{104}{\cancel{21}} \Rightarrow x = \frac{104}{21} \approx 4.95$$