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.
According to the Triangle Sum Theorem, the sum of the angles in a triangle is always 180 degrees. Therefore, we can set up the equation:
2x + 3x + 4x = 180
Combining like terms, we get:
9x = 180
Dividing by 9 on both sides, we find:
x = 20
Now, we can substitute x back into the expressions for the angles to find their measures:
2x = 2(20) = 40 degrees
3x = 3(20) = 60 degrees
4x = 4(20) = 80 degrees
Therefore, the smallest angle in the triangle measures 40 degrees.