1.based of the diagrams what is the the value of x? 2.how would you verify your answer for x

see below

Step-by-step explanation:

1.  x = 67

2.  We know that vertical angles are equal so the angle opposite it is equal to 67.  Call that angle y.  We also that that corresponding angles are equal if the lines are parallel. Angle y and angle x are corresponding angles. That means x is equal to y.  Since 67 = y and y =x   we know that 67=x

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4