SOLUTION: on line l, the measure of angle p=21x + 25 and the measure of angle n=675x-27/3 define the value of x and determine the measure of angle p and n in degrees ( the angles are supplem

Question 1124950: on line l, the measure of angle p=21x + 25 and the measure of angle n=675x-27/3 define the value of x and determine the measure of angle p and n in degrees ( the angles are supplementary if that helps )
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the fact that the angles are supplementary doesn't just help.
it's necessary.

p is the first angle.
n is the second angle.

since they're supplementary, their sun is 180 degrees, therefore:

p + n = 180

since p = 21x + 25 and n = 675x - 27/3, then:

p + n = 180 becomes 21x + 25 + 675x - 27/3 = 180.

since 25 = 75/3, the equation becomes 21x + 75/3 + 675x - 27/3 = 180.

combine like terms to get 696x + 48/3 = 180.

subtract 48/3 from both sides of the equation to get 696x = 180 - 48/3.

since 180 = 540/3, this equaiton becomes 696x = 540/3 - 48/3.

combine like terms to get 696x = 492/3.

solve for x to get x = 492 / 3 * 1 / 696 = .2356321839.

that's the value of x.

if that value of x is good, then 21x + 25 + 675x - 27/3 = 180 should be true when x = .2356321839.

evaluate this equati0on and you get 180 = 180, which is true.

this confirms the solution is correct.

your solution is:

x = .2356321839.

the first angle is 21 * x + 25 = 29.94827586 degrees.

the second angle is 675 * x - 27/3 = 150.0517241.

the sum of the angles is 29.94827586 + 150.0517241 = 180.

i used the numbers stored in the calculator and not what the calculator displayed, since what the calculator displays is a rounded version of the number stored in the calculator.

if i used the numbers displayed, i would have gotten the sum of the angles equals 29.94827586 + 150.0517241 = 179.99999996.

it's very close but it's not right on.
using the numbers stored in the calculator provides a more accurate answer.
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