Problem:
If ∠A is four times ∠B, and the complement of ∠B is four times the complement of ∠A, then ∠B=
Answer Choices:
A. 10∘
B. 12∘
C. 15∘
D. 18∘
E. 22.5∘
Solution:
Since ∠A=4∠B, and 90∘−∠B=4(90∘−∠A), it follows that 90∘−∠B=4(90∘−4∠B). Thus, ∠B=18∘.
Note. Observe that the two conditions
(1) ∠A is k times ∠B,
(2) the complement of ∠B is k times the complement of ∠A, imply that
∠A is the complement of ∠B.
Thus, we could solve ∠A+∠B=90∘ and ∠A=4∠B simultaneously for ∠B.