Two angles are said to be congruent if:
o
a. they share a side.
o
b. the sum of their measures is 180º.
o
c. they have the same angle measure.

Congruence is when two angles or shapes have the same shape and size. With angles, this means that two angles have the same angle measure. The correct answer is C.

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