Final answer:
To find the measure of angle ZLK, given that KM bisects ZLK and angle MKM = 4x - 3 and angle ZMK = 16 degrees, we solve for x and double the measure of ZMK to find that angle ZLK is 32 degrees.
Step-by-step explanation:
The task is to find the measure of angle ZLK. Given that KM bisects angle ZLK, this means that KM divides angle ZLK into two equal parts. Therefore, the measure of angle ZLK is twice the measure of angle ZMK.
Since the measure of angle MKM (MULKM) is given by the expression 4x - 3, and the measure of angle ZMK is given as 16 degrees, we can set up an equation to find the value of x:
4x - 3 = 16.
Solving for x:
Add 3 to both sides of the equation: 4x = 19.
Divide both sides by 4 to find x: x = 19/4 or
x = 4.75.
Since MKM (4x - 3) has been found to be 16 degrees just like angle ZMK, and KM bisects angle ZLK, it means angle ZLK is 16 + 16, which equals 32 degrees. Hence, the measure of angle ZLK (mZLK) is 32 degrees, which corresponds to option (d).