|
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.
|
|
|
| |
