The angles of a triangle measure 2x, 3x, and 4x. Using the Triangle Angle Sum Theorem, find the measure of the smallest angle in this triangle.

Answer 1

According to the Triangle Angle Sum Theorem, the sum of the angles in a triangle is always 180 degrees. Therefore, we can write an equation:

2x + 3x + 4x = 180

Simplifying the equation, we get:

9x = 180

Dividing both sides by 9, we get:

x = 20

Now we can find the measure of each angle by substituting x = 20:

The smallest angle is 2x = 2(20) = 40 degrees.