The image presents a geometric problem where triangle $ABC$ is given with certain conditions, and the task is divided into two parts:

1. Part (a) asks to find the length of side $AB$, which is equal to the length of side $BC$ (i.e., $AB = BC$).
2. Part (b) involves calculating an angle, particularly the angle $\angle ABC$, using the provided information about the angle $\angle BCD$, which is expressed as $(3x + 10)^\circ$.

The geometric setup includes:

• $\angle ABC = 30^\circ$,
• The external angle $\angle BCD = (3x + 10)^\circ$.

We can start by using the relationship between the angles in the triangle, and the fact that the external angle at vertex $C$ is equal to the sum of the remote interior angles.

Steps to solve:

1. From the triangle $ABC$, we know:

   • The angle sum of a triangle is always $180^\circ$.
   • $\angle ABC + \angle BAC + \angle ACB = 180^\circ$.

2. To solve for $x$ in part (a), we need to apply the fact that $AB = BC$, which makes the triangle isosceles. Therefore, $\angle BAC = \angle ACB$.

3. For part (b), we need to use the equation for the external angle at $C$ (i.e., $\angle BCD$).

Now, let's start solving these parts. Would you like to proceed with finding the value of $x$ or focus on a different aspect of the problem?