What is the measure of a, in degrees?

B

Step-by-step explanation:

Since AB = AC = 8 then the triangle is isosceles and

∠C = ∠B = 30° ( base angles of an isosceles triangle )

The sum of the 3 angles in a triangle = 180°

Subtract the sum of the base angles from 180, hence

∠A = 180° - (30 + 30)° = 180° - 60° = 120° → B

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