Question

I need help with finding Angle B

Answer 1

Check the picture below.

notice that, the diagonal is really just a traverse line cutting through the parallel segments of AB and DC, and since those angles are alternate interior ones, that means 5y - 1 = 7y - 15, and 6x - 6 = 4x + 2, therefore

$\bf 5y-1=7y-15\implies 14=2y\implies \cfrac{14}{2}=y\implies \boxed{7=y} \\\\\\ 6x-6=4x+2\implies 2x=8\implies x=\cfrac{8}{2}\implies \boxed{x=4}\\\\ -------------------------------\\\\ \measuredangle BAC = 5(7)-1\implies 34\qquad \measuredangle BCA=4(4)+2\implies 18 \\\\\\ therefore\qquad \measuredangle B=180-\measuredangle BAC-\measuredangle BCA$