SOLUTION: If 12 degrees less than one third of the larger is 4 degrees more than the smaller.Find the measure of each angle.

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.

RELATED QUESTIONS
The smaller of two supplementary angles is 30 degrees less than the measure of the larger (answered by Fombitz)

Two angles are supplementary. The measure of the smaller angle is 17 degrees more than... (answered by ozybloke)

Two angles are supplementary. The measure of the smaller angle is 13 degrees more than... (answered by mananth)

In a triangle the two larger angles differ by 10 degrees. The smaller angle is 50 degrees (answered by algebrahouse.com)

If one of two supplementay angles is 35 degrees larger than the other, find the measure... (answered by Fombitz)

Two angles are supplementary. The larger angle is eight degrees more than three times (answered by checkley79)

This one is a parralelogram: The 2 smaller angles of a parrallelogram have equal... (answered by hydromojo)

The measure of second triangle is 21 degrees more than measure of the first angle. The... (answered by pwac)