Question

I need to solve for x

Answer 1

Upper triangle: 12x +7x + angle of vertex = 180°
Lower triangle: 7x+6x+1 + angle vertex  =180°
Notice than the angles at the vertex are equal

Then: 12x+7x+angle of vertex =7x+6x+1+angle of vertex
19x =13x+1
6x=1 & x=1/6

Answer 2

6x+1 = 12x because the Z angles are the same

Solve this and you get:

1 = 12x - 6x => x = 1/6