What is the value of X in a triangle if it's 3x take 5 plus x plus 2x take 1 

In a triangle, the sum of the interior angles is always 180 degrees. From the problem, the three angles are given as:

1. \(3x - 5\)
2. \(x\)
3. \(2x - 1\)

We can write the equation for the sum of the angles as:

\[
(3x - 5) + x + (2x - 1) = 180
\]

Now, let's solve for \(x\):

1. Combine like terms:

\[
3x + x + 2x - 5 - 1 = 180
\]

\[
6x - 6 = 180
\]

2. Add 6 to both sides:

\[
6x = 186
\]

3. Divide both sides by 6:

\[
x = 31
\]

So, the value of \(x\) is 31.

Would you like any further details, or do you have any questions? Here are some related questions you might find interesting:

1. What are the actual measures of the angles in the triangle?
2. How would the solution change if one angle was given as an expression with a different sign?
3. What happens if the sum of the angles does not equal 180 degrees?
4. How would you solve for \(x\) if given a triangle's side lengths instead of angles?
5. Can you explain why the sum of angles in a triangle is always 180 degrees?

**Tip:** When solving equations involving angles, always remember to check that their sum matches the expected value for the shape, like 180 degrees for triangles.

What is the value of X in a triangle if it's 3x take 5 plus x plus 2x take 1?

Learn how to find the value of x in a triangle with angles 3x - 5, x, and 2x - 1. This step-by-step solution covers key geometry concepts and algebraic techniques, ideal for students in Grades 6-8.

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