The angles of a triangle measure 22, 32, and 4z. Using the Triangle Angle Sum Theorem, find the measure of the smallest angle in this triangle. (1 point)
The Triangle Angle Sum Theorem states that the sum of the angles in a triangle is always 180 degrees.
Given that the angles of the triangle measure 22, 32, and 4z, we can set up the equation:
22 + 32 + 4z = 180
Simplifying, we get:
54 + 4z = 180
Subtracting 54 from both sides, we get:
4z = 126
Dividing by 4, we get:
z = 31.5
Now we can find the measure of the smallest angle by substituting z back into the expression for the third angle:
4z = 4(31.5) = 126 degrees
Therefore, the smallest angle in this triangle measures 22 degrees.