Step-by-step explanation:
<QPR = <RST(given)
<PRQ = <TRS(vertically opposite angles)
<PQR = < STR (remaining angles)
triangles PQR~TRS (by A.A.A. axiom)
now
PR/RS = PQ/ST=QR/RT (corresponding sides of similar triangles are proportional)
or, 15/6=PQ/(2x-4)=x/RT
or, 15/6 = = PQ.RT=x.(2x-4)
or,, 15/6 = 2x²-4x
or, 15= 12x²-24x
or, 12x²-24x-15 = 0
or, 12x²-(30-6)x-15=0
or, 12x²-30x+6x-15=0
or, 2x(6x-15)+1(6x-15)=0
or, (6x-15)(2x+1)=0
Either,
6x-15 = 0
or, 6x = 15
so, x = 15/6
so, x = 2.5
or,
2x+1=0
2x=-1
or, x = -1/2
Value of x is either 2.5 or -1/2
