To solve the problem, we need to determine the angle measures of the triangle given by the expressions:

• $(8x - 1)^\circ$
• $(3x + 4)^\circ$
• $(3x + 9)^\circ$

The sum of the interior angles of a triangle is always $180^\circ$. Therefore, we can set up the equation:

$(8x - 1) + (3x + 4) + (3x + 9) = 180$

Now, solving for $x$:

1. Combine like terms: $8x + 3x + 3x - 1 + 4 + 9 = 180$ $14x + 12 = 180$

2. Subtract 12 from both sides: $14x = 168$

3. Divide by 14: $x = 12$

Now that we have $x = 12$, substitute it back into the expressions for the angles:

• $(8x - 1) = 8(12) - 1 = 96 - 1 = 95^\circ$
• $(3x + 4) = 3(12) + 4 = 36 + 4 = 40^\circ$
• $(3x + 9) = 3(12) + 9 = 36 + 9 = 45^\circ$

The three angles are $95^\circ$, $40^\circ$, and $45^\circ$.

The question asks which of the following is NOT one of the angle measures, and the options are:

• 45
• 85
• 95
• 40

The angle $85^\circ$ is not one of the triangle's measures. Therefore, the answer is 85.

Would you like more details or have any questions?

Here are 5 related questions:

1. What is the sum of the interior angles of any polygon?
2. How can you determine if a triangle is acute, obtuse, or right-angled?
3. What happens to the angles if the triangle is isosceles?
4. Can you form a triangle with angles that add up to less than 180°?
5. How would you solve if the triangle had angles given in radians instead of degrees?

Tip: Always check if the sum of the angles adds up to 180° to confirm the correctness of your solution for any triangle.