|
Question 849553: This is the problem I'm having trouble with:
"Find the value of each variable and the measure of each labeled angle."
I have two lines crossing like an X. The left is (3x + 8), the bottom is (5x + 4y), and the right is (5x - 20). And just so you know, I have tried to solve this problem, and I do know basically how to use the Vertical Angles Theorem. I'm just not sure how to do it when I have these two variables. I've tried to solve with the left and the bottom measures, as well as the right and the bottom measures, combining like terms, subtracting the numbers from both sides... but then I eventually get stuck at one of two points:
Left and bottom numbers: 8x + 4y = 180
Right and bottom numbers: 10x + 4y = 180
I have NO idea at all what I'm supposed to do with the 4y... If I subtracted it, then I would get 8x or 10x = 180 - 4y. Same thing when I'm trying to solve for X: I would get 4y = 180 - 10x or 8x. It's very likely that I am doing something wrong, maybe forgot something from Algebra that would be essential to solve this problem... but no matter how much I Google and look through my previous work for how I could solve this problem, I can't for the life of me figure out WHAT I am doing wrong. Hoping somebody can help :/
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! you have 2 lines that cross.
the left angle formed is equal to 3x + 8
the right angle formed is equal to 5x - 20.
the bottom angle formed is equal to 5x + 4y
since the lines are crossed, the opposite angles to each other are equal.
this means that:
3x + 8 = 5x - 20
solve for x to get x = 14 degrees.
the angle on the left side will be equal to 3(14) + 8 = 50 degrees.
the angle on the right side will be equal to 5(14) - 20 = 50 degrees.
this is at it should be since the angles are equal to each other.
since the sum of the 4 angles formed is equal to 360 degrees, the sum of the remaining 2 angles is equal to 260 degrees.
since those 2 angles are equal, then each one must be equal to 130 degrees.
one of those angles is equal to 5x + 4y.
you get 5x + 4y = 130
since x was already found to be 14, replace x with 14 to get:
5(14) + 4y = 130
solve for y to get y = (130 - 5(14)) / 4 which is equal to 15 degrees.
when x = 14 and y = 15, 5x + 4y = 5(14) + 4(15) = 70 + 60 = 130 which confirms the value of 15 for y is good.
your answers are:
x = 14 degrees
y = 15 degrees
2 of the angles measure 50 degrees each.
2 of the angles measure 130 degrees each.
|
|
|
| |
