Question 1153024
use the rule: Alternate Interior Angles are equal

pay attention to trapezoid made of two parallel lines, all given angles are its exterior angles

two alternate interior angles are equal (on shorter base of trapezoid) will be {{{4x}}} and {{{4x+8}}}
two alternate interior angles are equal (on greater base of trapezoid) will be {{{180-5x}}} and {{{180-(6x-10)=180-6x+10=190-6x}}}

the sum of all angles in trapezoid is {{{360}}}

so, 

{{{4x + (4x+8)+(180-5x)+(190-6x)=360}}}.......solve for {{{x}}}

{{{4x + 4x+8+180-5x+190-6x=360}}}

{{{8x-11x=360-180-8-190}}}

{{{-3x=-18}}}

{{{x=-18/-3}}}

{{{x=6}}}


{{{drawing ( 600, 600, -10, 10, -10, 10,
locate(0.3,2.8,5x), locate(0.5,4.5,4x),locate(6.7,4.5,4x+8),locate(7,2.6,6x-10),
locate(1,2.8,(180-5x)),locate(4.5,2.6,(190-6x)),locate(1.5,3.8,4x),locate(5.2,3.8,4x+8),
graph( 600, 600, -10, 10, -10, 10, 2,4,6, 3x, -6x+42)) }}}