In triangle JKL, if line JK is equal to line JL, angle J equals 23x-4, angle K equals 4x-1, and angle L equals 9x-31, find x and the measure of each angle.

Based on the information about side JK = side JL, then we know it is at least an isosceles triangle. Furthermore, ∡K =∡L because they are the base angles in an isosceles triangle.
Equation: 4x - 1 = 9x - 31
Solved: x = 6
Angle measures: ∡J = 23(6) - 4 = 138 - 4= 134
                            ∡K = ∡L = 23