Based on the measures provided in the diagram, determine the measure of ∠BDC. (You may assume thar point A is the center of the circle.)

A. 44 degrees
B. 46 degrees
C. 88 degrees
D. 92 degrees

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

something over 10 so ? /10

step-by-step explanation: