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To summarize:

If one quantity increases (decreases) as another quantity also increases (decreases), set ratios equal. If one quantity increases (decreases) as another quantity decreases (increases), set products equal.

The concept of proportion can be generalized to three or more ratios. A, B, and C are in the ratio 3:4:5 means AB = 34, AC = 35, and BC = 45.


In the figure to the right, the angles A, B, C of the triangle are in the ratio 5:12:13. What is the measure of angle A?

(A) 15
(B) 27
(C) 30
(D) 34
(E) 40

Since the angle sum of a triangle is 180°, A + B + C = 180. Forming two of the ratios yields
AB = 512     AC = 513

Solving the first equation for B yields
B = 125A

Solving the second equation for C yields
C = 135A

Hence, 180 = A + B + C = A + 125A + 135A = 6A . Therefore, 180 = 6A, or A = 30. The answer is choice (C).

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