SOLUTION: Find the value of each variable and the measure of each labeled angle. if two arrow are intersect each other. The top angle is (y+x) degree, on the left side angle is 2x degre

Algebra ->  Angles -> SOLUTION: Find the value of each variable and the measure of each labeled angle. if two arrow are intersect each other. The top angle is (y+x) degree, on the left side angle is 2x degre      Log On


   

Question 904683: Find the value of each variable and the measure of each labeled angle.

if two arrow are intersect each other. The top angle is (y+x) degree, on the left side angle is 2x degree, and the right angle is (y-x) degree.

How can I start and solve for the first step?


Thank you for your help. You are amazing!!!
Yen
Found 2 solutions by MathLover1, josgarithmetic:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

I think this is what you mean??
OK, when you look at the pairs of angles, you have two types of angles: linear pairs and vertical angles.
Linear pairs sum to 180 degrees.
Vertical angles are congruent (same measure).
In your diagram, the linear pairs are:
2x and y%2Bx
y%2Bx and y-x
The vertical angles are :
2x and y-x
So let's build equations using this information.
1.2x%2B%28y%2Bx%29=180
1.3x%2By=180

2.%28y%2Bx%29%2B%28y-x%29=180
2.2y=180
2.highlight%28y=90%29

3.2x=y-x
3.3x-y=0

Since eq. 2 solved for y, you can use either 1 or 3 to solve for x. You could also add eq. 1 and eq. 3,
3x%2By%2B%283x-y%29=180
6x=180
highlight%28x=30%29

So the three angles, given clockwise, are 2x=60, y%2Bx=120 degrees, and y-x=60 degrees.


Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The description suggests two rays forming vertical angles at the rays' intersection. Vertical angles are congruent. Does that help you? It should help. Also, any two adjacent angles are supplementary.