Final answer:
By using the interior angle measurements of triangle HIJ and the property that the sum of the interior angles in a triangle is 180 degrees, we can calculate the value of x and then find the measure of angle IJK to be 139 degrees.
Step-by-step explanation:
The question at hand requires the use of angle properties within a triangle and extended lines. In triangle HIJ, we know that the sum of the internal angles is always 180 degrees.
With the given measurements of angles, m∠JHI = (x+12)° and m∠HIJ = (x-3)°, we can establish an equation to solve for x by adding these angles and setting them equal to 180° minus the exterior angle m∠IJK.
Thus, we have x+12 + x-3 + (5x-6) = 180. Solving for x gives us x = 29°. Once x is found, we calculate m∠IJK by plugging x into the given expression for m∠IJK: m∠IJK = 5(29) - 6 = 139°.