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.(1 point)
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By the Triangle Angle Sum Theorem, the sum of the angles in a triangle is always 180 degrees.
Therefore, we can write the equation:
2x + 3x + 4x = 180
Simplifying this, we have:
9x = 180
Dividing both sides by 9, we get:
x = 20
Now we can substitute x back into our angle measures:
2x = 2(20) = 40 degrees
3x = 3(20) = 60 degrees
4x = 4(20) = 80 degrees
Therefore, the smallest angle in this triangle measures 40 degrees.