Answer:
x=70, y=55
Step-by-step explanation:
Since the angle "y" and 2x-15 form a straight line, that means the sum of the angles, must be 180 degrees.
So using this we can derive the equation: [tex]y+2x-15=180[/tex]
The next thing you need to know is that the sum of interior angles of a triangle is 180 degrees, so if we add all the angles, we should get 180.
So using these we can derive the equation: [tex]x+2y=180[/tex]
So, in this case we simply have a systems of equations. We can solve this by solving for x in the second equation (sum of interior angles), and plug that into the first equation.
Original Equation:
[tex]x+2y = 180[/tex]
Subtract 2y from both sides
[tex]x = 180-2y[/tex]
Now let's plug this into the first equation
[tex]y+2x-15=180[/tex]
Plug in 180-2y as x
[tex]y+2(180-2y)-15=180[/tex]
Distribute the 2
[tex]y+360-4y-15=180[/tex]
Combine like terms
[tex]-3y + 345 = 180[/tex]
Subtract 345 from both sides
[tex]-3y = -165[/tex]
Divide both sides by -3
[tex]y=55[/tex]
So we can plug this into either equation to solve for x
[tex]x+2y=180[/tex]
Substitute in 55 as y
[tex]x+2(55)=180[/tex]
[tex]x+110=180[/tex]
Subtract 110 from both sides
[tex]x=70[/tex]
