Answer:
x = 7
y = 3
Step-by-step explanation:
[tex]\triangle ABC[/tex] is an equilateral triangle so that means all sides are equal
which means
[tex]AB= BC=AC\\\\7=x[/tex]
now in [tex]\triangle ACD[/tex] is an isosceles triangle so that means opposite sides to the angles that have the same measure are equal
which means
[tex]AC=CD\\\\AC = y+4[/tex]
now remember that AC is a side of the equilateral [tex]\triangle ABC[/tex] so AC = 7
solving for y
[tex]7=y+4\\\\7-4 = y\\\\3=y[/tex]
so
[tex]x = 7\\\\y = 3[/tex]
