​ What is the exact angle measure in radians? 420

This is more than a complete circle....a complete circle is  2pi radians (or 360 degrees)...so you need a fraction that is greater than   2pi

  SO first and third options are no good.

 

Now as a ratio

 

420 is to 360     as   ? is to 2 pi     or:

420/360 = ? / 2pi

420/360 x 2pi = ?  = 840pi /360 = 7/3  pi