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
The Triangle Angle Sum Theorem states that the sum of the interior angles of a triangle is equal to 180 degrees.
Therefore, we can set up the equation:
2x + 3x + 4x = 180
Combine like terms:
9x = 180
Divide by 9:
x = 20
Now, we can find the measure of each angle:
Smallest angle: 2x = 2(20) = 40 degrees
Middle angle: 3x = 3(20) = 60 degrees
Largest angle: 4x = 4(20) = 80 degrees
Therefore, the smallest angle in this triangle measures 40 degrees.