1. **Problem statement:** Given a circle with center C and points A, B, D on the circumference, where $m\angle C = 35^\circ$, find: a) $m\angle LA$ b) $m\angle BD$ c) $m\angle BAD$ 2. **Relevant formula:** In a circle, the measure of an inscribed angle is half the measure of its intercepted arc. Also, the central angle equals the measure of the arc it intercepts. 3. **Step-by-step solution:** 1. Since $m\angle C = 35^\circ$ is a central angle, the arc $AB$ it intercepts measures $35^\circ$. 2. The inscribed angle $m\angle LA$ intercepts the same arc $AB$, so: $$m\angle LA = \frac{1}{2} \times 35^\circ = 17.5^\circ$$ 3. For $m\angle BD$, assuming it is an inscribed angle intercepting arc $AD$, and since $m\angle BAD$ is also asked, we need more information or assumptions. However, typically, $m\angle BD$ is equal to half the measure of the arc it intercepts. 4. Without additional arc measures, we cannot find exact values for $m\angle BD$ and $m\angle BAD$. **Final answer:** $$m\angle LA = 17.5^\circ$$ Other angles require more information to solve.