Answer:
x=7
y=4
Explanation:
Since 3x-5 and 5y-4 are sides of an equilateral triangle then...
3x-5=5y-4
3x-5 and y+12 are also sides of an isosceles triangle. Using the angles that are given to us we can find that...
3x-5=y+12
We can use substitution to substitute 5y-4 for 3x-5...
5y-4=y+12
Move like terms to one side
4y=16
Divide both sides by 4
y=4
Plug y=4 back into either of the two equations
3x-5=5(4)-4
3x-5=20-4
3x-5=16
Add 5 to both sides
3x=21
Divide both sides by 3
x=7
x=7
y=4