In the above figure, m∠A = 20° and m∠B = 2x + 18. If angles A and B are complementary angles, what are the value of x and the measure of angle B?
A. x = 71, m∠B = 160°
B. x = 26, m∠B = 52°
C. x = 26, m∠B = 70°
D. x = 46, m∠B = 70°

step-by-step explanation:

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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

3

step-by-step explanation: