If ∠ A is four times ∠ B, and the complement of ∠ B is four times the complement of ∠ A, then ∠ B=

1994 AMC 12 Problem 9

Attempt Problem 9 of the 1994 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1994 AMC 12 solutions, or check the answer key.

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\angle A

is four times

\angle B,

and the complement of

\angle B

is four times the complement of

\angle A,

then

\angle B=

10^\circ

12^\circ

15^\circ

18^\circ

22.5^\circ

Let

\angle B=x

and write

\angle A=4x

Translate the second condition as

90-x=4(90-4x)

Let

\angle B=x,

\angle A=4x.

The complement condition gives

90-x=4(90-4x).

Hence

15x=270

and

x=18^\circ.

Thus the correct answer is D.