Answer:
The answer is x = 13 and y = 5.
Step-by-step explanation:
From the diagram, we know that there are two congruent legs of the triangle on the left (indicated by the lines). This means that two angles in this triangle measure 5x degrees. Because the third angle of the triangle is supplementary to the 130 degree angle, we know it must measure (180-130) or 50 degrees. We can apply this supplementary argument to the triangle on the right as well. Looking at both triangles, we can create the following equations using the idea that the interior angles of a triangle must add to 180 degrees total. This gives us the following equations:
5x + 5x + 50 = 180
10y + 5 + 6x - 3 + 50 = 180
Let's begin by solving the first equation, since it only contains one variable.
5x + 5x + 50 = 180
We can start by combining like terms on the left side of the equation.
10x + 50 = 180
Then, we can subtract 50 from both sides of the equation.
10x = 130
Next, we can divide both sides by 10.
x = 13
Now that we know the value for x, we can take our second equation (that came from the triangle on the right side) and solve for y.
10y + 5 + 6x - 3 + 50 = 180
Let's begin by simplifying the equation a little bit.
10y + 6x + 52 = 180
We can subtract 52 from both sides of the equation.
10y + 6x = 128
Now we can plug in the value for x we found above, x = 13, and simplify.
10y + 6(13) = 128
10y + 78 = 128
We should then subtract 78 from both sides of the equation.
10y = 50
Finally, we can divide both sides of the equation by 10.
y = 5
Therefore, the answer to the problem is x = 13 and y = 5.
Hope this helps!
