Final answer:
To find the value of 'x' when ⟒KM bisects ⟒LKJ, we set the angle measurements equal to each other and solve the equation, resulting in 'x' being equal to 3.
Step-by-step explanation:
If ⟒KM bisects ⟒LKJ, the measure of angle LKM (m⟒LKM) and the measure of angle MKJ (m⟒MKJ) should be equal because the ray ⟒KM divides ⟒LKJ into two congruent angles. Therefore, we can set the measures of these angles equal to each other to solve for 'x':
(5x+24)° = (9x+12)°
To find the value of 'x', we solve this equation:
5x + 24 = 9x + 12
Subtracting 5x from both sides gives:
24 = 4x + 12
Now, subtract 12 from both sides:
12 = 4x
Dividing both sides by 4 yields:
3 = x
Thus, the value of 'x' is 3.