Question

The angles of a triangle measure 2x , 3x , and 4x . Using the Triangle Angle Sum Theorem, the equation to solve for x is: 2x+3x+4x=180 .

Solve the equation for x . What is the measurement of the smallest angle?

(2 points)
The value of x is
. The measurement of the smallest angle is
degrees.

Answer 1

To solve for \( x \) using the equation derived from the Triangle Angle Sum Theorem, we have:

\[
2x + 3x + 4x = 180
\]

Combining the terms on the left side gives:

\[
9x = 180
\]

Next, we solve for \( x \) by dividing both sides by 9:

\[
x = \frac{180}{9} = 20
\]

Now, we can find the measurements of the angles in the triangle:

1. The first angle is \( 2x = 2(20) = 40 \) degrees.
2. The second angle is \( 3x = 3(20) = 60 \) degrees.
3. The third angle is \( 4x = 4(20) = 80 \) degrees.

Thus, the smallest angle is \( 40 \) degrees.

So, the final answers are:

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