a. The equation that would help solve for the missing angle measures is:
(12x + 1) + 3x + (16x - 7) = 180
b. To solve the equation, we need to combine like terms:
12x + 1 + 3x + 16x - 7 = 180
(12x + 3x + 16x) + (1 - 7) = 180
31x - 6 = 180
Next, we need to isolate the variable x by using inverse operations.
Adding 6 to both sides:
31x = 186
Finally, divide both sides by 31:
x = 6
Now that we have the value of x, we can substitute it back into the original expressions to find the measure of each angle.
m∠J = 12x + 1 = 12(6) + 1 = 73 degrees
m∠K = 3x = 3(6) = 18 degrees
m∠L = 16x - 7 = 16(6) - 7 = 89 degrees