The angle of a triangle measures 2x, 3x, and 4x degrees . Using the triangle angle sum theorem, find the measure of the smallest angle in this triangle
The sum of the angles in a triangle is always 180 degrees.
Let the angles of the triangle be 2x, 3x, and 4x degrees.
According to the triangle angle sum theorem,
2x + 3x + 4x = 180
9x = 180
x = 180/9 = 20
Therefore, the measure of the smallest angle in this triangle is 2x = 2(20) = 40 degrees.