Question 46·Hard·Geometry and Trigonometry

A transversal intersects two parallel lines, forming four congruent acute angles and four congruent obtuse angles.

The measure of one of the acute angles is $(8x - 22)^\circ$.

The sum of the measures of four of the acute angles and one of the obtuse angles is $(24x + w)^\circ$.

What is the value of $w$?