Meeting the condition for annulment of marriage in Illinois

I am an immigrant to the US and got married in Illinois last year. Recently, I learned that my family in my home country, following our cultural traditions, had already contracted a marriage on my behalf even before my marriage here in the US. I have agreed with my wife here in the US that the best course of action is to annul our marriage while I seek resolution to the cultural implications of the earlier marriage since it poses a major danger to unity in my family and prospects of success in my current marriage. Does this condition satisfy the criteria of bigamy for annulment of marriage in Illinois? Note: there is no cultural requirement that I consent to the earlier marriage, which is binding in my home country. Thanks!