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.

Answer 1

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.