The angles of a triangle measure 2x, 3x, and 4x. Using the triangle sum theorem find the measure of the smallest angle in this triangle .
The sum of the angles in a triangle is always 180 degrees. Therefore, we can set up the equation:
2x + 3x + 4x = 180
Combining the like terms, we get:
9x = 180
Now, we can solve for x:
x = 180/9
x = 20
Now that we know x = 20, we can find the measure of each angle:
2x = 2(20) = 40 degrees
3x = 3(20) = 60 degrees
4x = 4(20) = 80 degrees
Therefore, the smallest angle in this triangle measures 40 degrees.