Question

The angles of a triangle measure 2x, 3x, and 4x. Using the triangle angle sum, the equation to solve for x is: 2x + 3x + 4x = 180. Solve the equation for x. What is the measurements of the smallest angle? The value of x is what. The measurement of the smallest angle is what degrees.

Answer 1

To solve the equation \(2x + 3x + 4x = 180\):

1. Combine the like terms on the left side:
\[
2x + 3x + 4x = 9x
\]
So the equation becomes:
\[
9x = 180
\]

2. Now divide both sides by 9 to solve for \(x\):
\[
x = \frac{180}{9} = 20
\]

Now that we have \(x = 20\), we can find the measures of the angles:

- The first angle is \(2x\):
\[
2x = 2(20) = 40^\circ
\]

- The second angle is \(3x\):
\[
3x = 3(20) = 60^\circ
\]

- The third angle is \(4x\):
\[
4x = 4(20) = 80^\circ
\]

Now, we can summarize the findings:
- The value of \(x\) is \(20\).
- The measurements of the angles are \(40^\circ\), \(60^\circ\), and \(80^\circ\).
- The smallest angle is \(40^\circ\).

In conclusion:
- The value of \(x\) is \(20\).
- The measurement of the smallest angle is \(40\) degrees.