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Example of ratio problem solving 1
Question:
The ratio of two supplementary angles is one to five. Find the measure of each angle.
Solution:
The measure of the small angle is x
The measure of the large angle is 5x
The ratio of the small angle to the large angle is 1 : 5 (note: 1x/5x = 1/5)
The sum of two supplementary angles is 180o
so we get the equation:
x + 5x = 180o
6x = 180o
x = 30o
5x = 5(30o) = 150o
so the small angle is 30o and the large angle is 150o

What is the definition of the supplementary angles? If two angles are supplementary, then the sum of them is 180o. Since the ratio of the small angle to the large angle is 1:5. So let the small angle be x, the the large angle will be 5x. Then we get the equation x + 5x = 180o. Combine similar (like) terms, to get the standard form ax = b, then x = b/a. Check if the result satisfy the equation. If yes, then the result is the solution of given problem.