Question

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 of a triangle is always 180 degrees.

Therefore, we can write the equation:

2x + 3x + 4x = 180

Combining like terms, we get:

9x = 180

Dividing by 9 on both sides gives us:

x = 20

Now, we can find the measure of the smallest angle which is represented by 2x.

Therefore,

2x = 2(20) = 40

So, the smallest angle in this triangle measures 40 degrees.