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Let's solve for the measure of \( \angle BCA \).

Given in the problem:
- \( \angle A = (2x + 18)^\circ \)
- \( \angle B = (2x - 6)^\circ \)
- \( \angle ACD = (6x - 8)^\circ \)

Since \( \angle BCA \) is part of a straight line along with \( \angle ACD \), we can use the fact that these two angles are supplementary:
\[
\angle BCA + \angle ACD = 180^\circ
\]

### Step 1: Set up the equation
Since \( \angle ACD = (6x - 8)^\circ \), we have:
\[
\angle BCA + (6x - 8) = 180
\]

### Step 2: Solve for \( x \) using angle properties
If the given angles \( \angle A \), \( \angle B \), and \( \angle C \) (which corresponds to \( \angle BCA \)) form a triangle, they must add up to \( 180^\circ \). Therefore:
\[
(2x + 18) + (2x - 6) + \angle BCA = 180
\]

Let me know if you want me to continue solving for \( x \) and finding the measure of \( \angle BCA \).

In the diagram below, \( \angle A = (2x + 18)^\circ \), \( \angle B = (2x - 6)^\circ \), and \( \angle ACD = (6x - 8)^\circ \). What is the measure of \( \angle BCA \)?

This geometry problem involves finding the measure of \( \angle BCA \) using angle properties and supplementary angles in a triangle. Given \( \angle A = (2x + 18)^\circ \), \( \angle B = (2x - 6)^\circ \), and \( \angle ACD = (6x - 8)^\circ \), learn the step-by-step solution to determine \( \angle BCA \).

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