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.

Answer 1

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.