https://file.aiquickdraw.com/mathbot/file/17278395047260ja2vs25.jpg

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.

Which of the following is NOT one of the angle measures?

Learn how to solve for the angles of a triangle using algebraic expressions, with a step-by-step solution. This problem covers key algebraic concepts and the Triangle Angle Sum Theorem. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation