1. **State the problem:** We need to find the measure of angle $a$ formed by two intersecting chords inside a circle. 2. **Formula:** When two chords intersect inside a circle, the measure of the angle formed is half the sum of the measures of the intercepted arcs. Mathematically, this is: $$a = \frac{b + c}{2}$$ where $b$ and $c$ are the measures of the intercepted arcs. 3. **Given values:** - Arc $b = 41^\circ$ - Arc $c = 29^\circ$ 4. **Calculate the sum of arcs:** $$b + c = 41 + 29 = 70$$ 5. **Apply the formula:** $$a = \frac{70}{2}$$ 6. **Simplify the fraction:** $$a = \frac{\cancel{70}}{\cancel{2}} = 35$$ 7. **Final answer:** The measure of angle $a$ is **35 degrees**.