A. Find the Measure of the Central Angle 1. Problem: Given the intercepted arc measures 72° in a circle, find the measure of the central angle. Step 1: Recall that the measure of a central angle is equal to the measure of its intercepted arc. Step 2: Therefore, the central angle = 72°. 2. Problem: Given the central angle measures 110°, find the measure of the intercepted arc. Step 1: The intercepted arc measure is equal to the central angle measure. Step 2: So, intercepted arc = 110°. 3. Problem: The intercepted arc measures $\frac{3}{5}$ of a circle. Find the measure of the central angle. Step 1: A full circle measures 360°. Step 2: Calculate arc measure: $\frac{3}{5} \times 360 = 216°$. Step 3: Since central angle equals the arc measure, central angle = 216°. 4. Problem: The central angle measures 45°. Find what fraction of the circle's circumference its arc represents. Step 1: The fraction of the circle is the ratio of the central angle to the full circle. Step 2: Fraction = $\frac{45}{360} = \frac{1}{8}$. 5. Problem: A circle has radius 10 cm and central angle 60°. Find the length of the arc. Step 1: Formula for arc length: $\text{arc length} = r \times \theta$ (in radians). Step 2: Convert 60° to radians: $60° = \frac{60 \pi}{180} = \frac{\pi}{3}$ radians. Step 3: Calculate arc length: $10 \times \frac{\pi}{3} = \frac{10\pi}{3}$ cm. B. Find the Measure of the Inscribed Angle 6. Problem: The intercepted arc measures 80°. Find the measure of the inscribed angle. Step 1: The inscribed angle is half the measure of its intercepted arc. Step 2: Inscribed angle = $\frac{80}{2} = 40°$. 7. Problem: The inscribed angle measures 35°. Find the measure of its intercepted arc. Step 1: The intercepted arc measure is twice the inscribed angle. Step 2: Arc measure = $2 \times 35 = 70°$. 8. Problem: An inscribed angle intercepts an arc of 120°. Find the angle's measure. Step 1: Inscribed angle = half of intercepted arc. Step 2: Angle = $\frac{120}{2} = 60°$.