The problem asks for the measure of $\angle A$ in the triangle, and we are given the following information:

• Triangle $ABC$ with $AB = AC = 8$ (this is an isosceles triangle).
• $\angle ACB = 30^\circ$.

Step-by-step solution:

Since $AB = AC$, triangle $ABC$ is an isosceles triangle. In an isosceles triangle, the angles opposite the equal sides are also equal. So, $\angle ABC = \angle ACB = 30^\circ$.

Using the fact that the sum of the angles in any triangle is $180^\circ$, we can calculate $\angle A$ as follows:

$\angle A = 180^\circ - \angle ABC - \angle ACB$

Substitute the values:

$\angle A = 180^\circ - 30^\circ - 30^\circ = 120^\circ$

Thus, the measure of $\angle A$ is $120^\circ$.

The correct answer is:

B. 120°

Would you like more details or have any questions?

Here are 5 related questions to explore:

1. How do we determine if a triangle is isosceles?
2. What are the properties of an isosceles triangle?
3. How can you verify the sum of interior angles in any triangle?
4. What is the exterior angle theorem and how can it apply here?
5. How would the calculation change if $\angle ACB$ was a different value?

Tip: Always remember that the sum of the interior angles in any triangle is $180^\circ$.