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

The Triangle Angle Sum Theorem states that the sum of the angles in a triangle is 180 degrees.

Therefore, we can write the equation:

2x + 3x + 4x = 180

Combining like terms, we have:

9x = 180

Dividing both sides by 9, we have:

x = 20

To find the measure of the smallest angle, we substitute this value back into the equation for the smallest angle:

2(20) = 40 degrees

Therefore, the measure of the smallest angle in this triangle is 40 degrees.