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To solve this problem, we need to determine the measure of each indicated angle in the triangle \( \triangle ABC \) by finding the value of \( x \).

### Step 1: Set up the Equation
Since \( \triangle ABC \) is a triangle, the sum of the interior angles should equal \( 180^\circ \). Given the angles:
- \( \angle CAB = (6x + 1)^\circ \)
- \( \angle ACB = (8x + 16)^\circ \)
- \( \angle ABC = (15x + 9)^\circ \)

We can write the equation:
\[
(6x + 1) + (8x + 16) + (15x + 9) = 180
\]

### Step 2: Solve for \( x \)
Combine like terms:
\[
6x + 8x + 15x + 1 + 16 + 9 = 180
\]
\[
29x + 26 = 180
\]

Subtract 26 from both sides:
\[
29x = 154
\]

Divide by 29:
\[
x = 5.31
\]



Determine the measure of each indicated angle in the triangle by finding the value of x, given the angles are (6x + 1)°, (8x + 16)°, and (15x + 9)°.

Determine the measure of each angle in a triangle by finding x using algebra. Given angles (6x + 1)°, (8x + 16)°, and (15x + 9)°, find the values of x and the individual angles. This problem uses the Triangle Sum Theorem, making it ideal for Grade 9 students.

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