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To solve for the measure of \( \angle A \), let's analyze the triangle.

The triangle \( ABC \) shown is an isosceles triangle, as two sides \( AB \) and \( AC \) have equal lengths (8 units). Given that \( \angle C = 30^\circ \), we can use the properties of isosceles triangles to determine \( \angle A \).

### Steps:

1. In an isosceles triangle, the two base angles are congruent. Therefore, \( \angle A \) and \( \angle B \) are equal.

2. The sum of the angles in any triangle is always \( 180^\circ \). So:
   \[
   \angle A + \angle B + \angle C = 180^\circ
   \]
   Since \( \angle A = \angle B \), we can express the equation as:
   \[
   2\angle A + 30^\circ = 180^\circ
   \]

3. Solving for \( \angle A \):
   \[
   2\angle A = 180^\circ - 30^\circ = 150^\circ
   \]
   \[
   \angle A = \frac{150^\circ}{2} = 75^\circ
   \]

Therefore, the measure of \( \angle A \) is \( 75^\circ \). However, none of the provided options directly matches \( 75^\circ \), and it seems the options are either incorrectly provided, or the exact question wording might be different from typical multiple-choice formats.

Do you have any questions or need further details?

### Related Questions:
1. What is the sum of the interior angles of any triangle?
2. How do we solve for unknown angles in isosceles triangles?
3. Can you use the sine or cosine rule to solve non-right triangles?
4. Why is it important for the base angles of isosceles triangles to be equal?
5. How would you find the missing angles if you only had side lengths?

### Tip:
Always check if a triangle is isosceles or equilateral, as knowing this can simplify angle calculations.

Learn how to find the measure of an angle in an isosceles triangle when given the length of the sides and one of the angles. This problem involves the isosceles triangle theorem and the sum of angles in a triangle, suitable for Grades 8-10.

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