ΔABC has two congruent angles. Therefore, it is an isosceles triangle.
Therefore we have the equation (1) 3x - 5 = y + 12.
All angles of the ΔDBC are congruent. Therefore it is an equilateral triangle.
Therefore we have the equation (2) 3x - 5 = 5y - 4
From (1) and (2) we have the equation:
5y - 4 = y + 12 add 4 to both sides
5y = y + 16 subtract y from both sides
4y = 16 divide both sides by 4
y = 4
Substitute the value of y to (1):
3x - 5 = 4 + 12
3x - 5 = 16 add 5 to both sides
3x = 21 divide both sides by 3
x = 7
Answer: x = 7 and y = 4