10 point! ! not b, i already tried. which relationship is always correct for the angles p, q, and r of triangle abc? a p + r = q b p + q + r = 180 degrees c p + q + r = 90 degrees d q + r = p

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

answer: 7

step-by-step explanation: