One rule in Geometry is the vertical angle theorem. This is when two angles are directly across from each other, they would equal each other. This means that (3x+54) and (7x+10) will equal each other, giving you the function
3x+54=7x+10
Knowing this, all we would need to do now is solve for x. To do this, lets get x to the left. We do this but subtracting both sides by 7x to get rid of 7x on the right side, and bring it to the left
3x+54=7x+10 ------> 3x-7x+54=10 --------> -4x+54=10
Now, lets get x by itself, but subtracting both sides by 54, then dividing both sides by -4
-4x+54=10 ---> -4x=10-54 ---> -4x=-44 ---> x=-44/-4 ---> x= 11
So, we know that x=11. Now, we can plug it into either function. It doesn't matter which one since they both equal each other
f(x)=7x+10 ---> f(11)=7(11)+10 = 77+10 = 87
Our answer is 87
