The angles of a triangle measure 2x, 3x, and 4x. Using the Triangle Angle Sum Theorem, find the measure of the smallest angle in this triangle.(1 point)

Question

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Answer 1

According to the Triangle Angle Sum Theorem, the sum of the angles in a triangle is 180 degrees. In this triangle, the angles are given as \(2x\), \(3x\), and \(4x\).

We can set up the equation:

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

Combining the terms on the left gives:

\[ 9x = 180 \]

Now, solve for \(x\):

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

Now we can find the measures of the angles:

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

The smallest angle is \(40\) degrees.

Thus, the measure of the smallest angle in this triangle is:

\[ \boxed{40} \] degrees.