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Question 340301: If 12 degrees less than one third of the larger is 4 degrees more than the smaller.Find the measure of each angle.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! Let x be the smaller.
Let y be the larger.
1/3 * y - 12 = x + 4
Add 12 to both sides of the equation to get:
1/3 * y = x + 16
Multiply both sides of the equation by 3 to get:
y = 3x + 48
For every value of x, y can be found using that formula, it seems.
If x = 1, then y = 51
If x = 2, then y = 54
If x = 3, then y = 57
To test this out, substitute in the original equations.
The original equation states:
12 degrees less than one third of the larger is 4 degrees more than the smaller.
If the larger is 57, then 1/3 of that is 19 and 12 less than that is 7. Since 7 is 4 more than 3, the equation holds.
If the larger is 51, then 1/3 of that is 17 and 12 less than that is 5. Since 5 is 4 more than 1, the equation holds.
Your solution does not lend itself to one unique angle.
The value of each angle is dependent on the value of the other.
Assume the larger angle is 85 degrees.
1/3 of 85 = 28 and 1/3 degrees.
12 less than is 16 and 1/3 degrees.
4 more than that is 20 and 1/3 degrees.
If the larger angle is 85 degrees, then the smaller angle has to be 20 and 1/3 degrees.
Working backward, 20 and 1/3 degrees minus 4 = 16 and 1/3 degree.
12 more than that is 28 and 1/3 degrees.
3 times that is 84 and 3/3 degrees which is equal to 85 degrees.
The angles can be anything as long as they keep the fixed relationship between them represented by the formula.
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