The value of x is 5
Explanation
Given <ACD=2x+4
<ACB=5x-11
Given that ABCD is a rhombus. So the opposite angles will be same and all the sides will be equal.
[tex]AB=BC=CD=AD\\<A=<C\\<B=<D=y\\<C=<ACD+<ACB\\<C=2x+4+5x-11\\[/tex]
diagonal AC divides the rhombus into two triangles ACD and ACB
according to angle sum property, the sum of all angles of a triangle is 180.
consider triangle ACD
[tex]<DAC+<DCA+<D=180\\2x+4+2x+4+y=180\\4x+8+y=180(1)\\<CAB+<ACB+<B=180\\5x-11+5x-11+y=180\\10x-22+y=180(2)\\\\\\\\comparing (1) &(2)\\4x+8+y=10x-22+y\\6x=30\\x=30/6=5[/tex]
