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)
______° What is the CORRECT answer bot?
To find the measure of the smallest angle in the triangle, we can use the Triangle Angle Sum Theorem, which states that the sum of all angles in a triangle is always 180 degrees.
Let's denote the smallest angle as 2x, the second angle as 3x, and the largest angle as 4x. The sum of these angles is given by:
2x + 3x + 4x = 180
Combining like terms, we have:
9x = 180
To solve for x, we divide both sides by 9:
9x/9 = 180/9
x = 20
Now, we can find the measure of the smallest angle by substituting x = 20 into 2x:
2x = 2(20) = 40
Therefore, the measure of the smallest angle in this triangle is 40 degrees.