**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 $\frac{A}{B}$ = $\frac{3}{4}$, $\frac{A}{C}$ = $\frac{3}{5}$, and $\frac{B}{C}$ = $\frac{4}{5}$.

**Example:**

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 180Â°,

$\frac{A}{B}$ = $\frac{5}{12}$ $\frac{A}{C}$ = $\frac{5}{13}$

Solving the first equation for B yields

B = $\frac{12}{5}$A

Solving the second equation for C yields

C = $\frac{13}{5}$A

Hence, 180 =

*A + B + C*= 180. Forming two of the ratios yields$\frac{A}{B}$ = $\frac{5}{12}$ $\frac{A}{C}$ = $\frac{5}{13}$

Solving the first equation for B yields

B = $\frac{12}{5}$A

Solving the second equation for C yields

C = $\frac{13}{5}$A

Hence, 180 =

*A + B + C = A*+ $\frac{12}{5}$*A*+ $\frac{13}{5}$*A*= 6*A*. Therefore, 180 = 6*A*, or*A*= 30. The answer is choice (C).