1. **Problem statement:** Given a circle with center O and points C, B, A, D on the circumference, the measure of angle CDB is 57°. We need to find the measure of angle CDA. 2. **Relevant theorem:** In a circle, the measure of an inscribed angle is half the measure of its intercepted arc. 3. **Step 1:** Angle CDB intercepts arc CB. Since angle CDB = 57°, the measure of arc CB is twice that: $$\text{arc } CB = 2 \times 57^\circ = 114^\circ$$ 4. **Step 2:** Angle CDA intercepts arc CA. Points C, B, A, D lie on the circle, so arcs CB and CA together form arc CA plus arc AB. Since the circle is 360°, the arcs around point D satisfy: $$\text{arc } CA = 360^\circ - \text{arc } CB = 360^\circ - 114^\circ = 246^\circ$$ 5. **Step 3:** The measure of angle CDA is half the measure of arc CA: $$\angle CDA = \frac{1}{2} \times 246^\circ = 123^\circ$$ 6. **Answer:** The measure of angle CDA is **123°**.