One of the properties of a parallelogram is that its diagonals bisect each other. This means that one diagonal cuts the second diagonal in equal length.
This means that AP = PC. If AP = PC, then 45 = 3x + 15.
[tex]45=3x+15[/tex]
We can now find the value of x using the equation above.
First, subtract 15 on both sides of the equation.
[tex]45-15=3x+15-15[/tex][tex]30=3x[/tex]
Then, divide both sides of the equation by 3 to isolate x.
[tex]\frac{30}{3}=\frac{3x}{3}[/tex][tex]10=x[/tex]
Therefore, the value of x is 10. (Option B)
