The angles of a triangle measure 2x, 3x, and 4x. Using the Triangle Angle Sum Theorem, find the angle of the smallest angle in the triangle.
The Triangle Angle Sum Theorem states that the sum of the three angles in a triangle is always 180 degrees.
So, we can set up the equation:
2x + 3x + 4x = 180
Simplifying:
9x = 180
Dividing by 9 on both sides:
x = 20
Now, we can substitute x back into the smallest angle (2x) to find the measure of the angle:
2(20) = 40 degrees
Therefore, the smallest angle in the triangle measures 40 degrees.