In the figure below, solve for β (beta, top left angle). β = _ degrees (round answer to the nearest tenth and do NOT include units in your answer)

good job you smart son of a gun you are smarter that einstein. 7

i think that you should ask google for the answer to that problem because if we don't know it google does

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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