Is 15 deductive or inductive reasoning (geometry)

Hi again!

I answered the one for number 16, so ill do this one as well :)

I would say that number 15 would be deductive

The definition for deductive reasoning is the art of deriving new geometric facts from previously-known facts by using logical reasoning

She already knew about the other degrees, so those were previously-known facts.

Hope this helped!

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