Final answer:
The measure of angle mZBCL is 9 degrees if mZBCL is meant to be mBCL. This is determined by setting up an equation with the given angle measures and solving for x, which is then used to find mBCL.
Step-by-step explanation:
To find the measure of angle mZBCL, we need to use the given expressions and the fact that the sum of angles in linear pair is equal to 180 degrees. Since we have mBCD = 171° and mBCD and mBCL form a linear pair, their measures add up to 180°.
We set up the equation: mBCD + mBCL = 180°. By substituting the given values, we get 171° + (x + 58) = 180°.
Solving for x gives us:
x + 58 + 171 = 180
x + 229 = 180
x = 180 - 229
x = -49°
Since angle measures cannot be negative and mBCD = 171°, it means that mZLCD and mZBCL must be referring to the angles in different locations or is potentially a typo. If mZBCL is mBCL, then we can now find its measure by substituting x back into mBCL = x + 58:
mBCL = (-49) + 58 = 9°
Therefore, mZBCL is 9 degrees if mZBCL is meant to represent mBCL.