Find the value of angle a.

Let's analyze the problem step by step. 1. We are given a circle with center O. Points B, D, and E lie on the circumference of the circle. 2. Angle $$\angle BOD$$ is the central angle, and its measure is given as $$118^{\circ}$$. 3. Angle $$\angle BED$$ is an inscribed angle that intercepts the same arc, BD, as the central angle $$\angle BOD$$. 4. The inscribed angle theorem states that the measure of an inscribed angle is half the measure of its intercepted central angle. Therefore, the measure of angle $$\angle BED$$ (which is 'a') is half the measure of angle $$\angle BOD$$. 5. We can write this relationship as: $$\angle BED = \frac{1}{2} \cdot \angle BOD$$ 6. Substituting the given value of $$\angle BOD = 118^{\circ}$$, we get: $$\angle BED = \frac{1}{2} \cdot 118^{\circ} = 59^{\circ}$$ Therefore, the value of angle a ($$\angle BED$$) is $$59^{\circ}$$. Answer: 59