Find angle a if arc mde is equal to 50 degrees and arc mbc is equal to 10 degrees

m∠A = (1/2)(mDE - mBC)

m∠A=(1/2)(50-10) = (1/2)*40=20

m∠A = 20

its kind of blurry. can you put a clearer pic?

step-by-step explanation:

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