1. The problem involves finding the measures of arcs and angles related to central angles in circles. 2. Recall that a central angle in a circle is an angle whose vertex is the center of the circle and whose sides are radii. 3. The measure of a central angle is equal to the measure of the intercepted arc. 4. For Figure 1, the central angle at C is given as 50°. 5. a) Arc DB corresponds to the central angle 50°, so $\text{arc } DB = 50^\circ$. 6. b) Arc ADB is the major arc that includes arc DB and the rest of the circle. Since a full circle is 360°, $\text{arc } ADB = 360^\circ - 50^\circ = 310^\circ$. 7. c) Arc AD is the same as arc DB because points A and D are endpoints of the arc opposite to B, so $\text{arc } AD = 50^\circ$. 8. d) Angle DAB is an inscribed angle that intercepts arc DB. The measure of an inscribed angle is half the measure of its intercepted arc, so $\angle DAB = \frac{1}{2} \times 50^\circ = 25^\circ$. Final answers: - 1a) $\text{arc } DB = 50^\circ$ - 1b) $\text{arc } ADB = 310^\circ$ - 1c) $\text{arc } AD = 50^\circ$ - 1d) $\angle DAB = 25^\circ$