Winter Geometry problem 1

Solution 1: draw line $L_3$ perpendicular to both $L_1$ and $L_2,$ making a pentagon with the other lines. The angles of a pentagon always add to $540^\circ,$ so $w = 540^\circ-180^\circ-126^\circ-(180^\circ-58^\circ) = \boxed{112^\circ}$

Solution 2: draw line $L_3$ parallel to $L_1$ and passing through point $W.$ This is a simple transversal problem. $w = a + (180^\circ - b)$ $w = 58^\circ + 54^\circ = \boxed{112^\circ}$