Base radius = 5cm, Height = 12 cm. So Slant Height = 13cm.
If, we open it now then it appears as an arc with its radius = Slant Height of the cone = 13 cm.
Length of the arc = Circumfernce of the cone = 2×pie×5 = 10 pie cm
Now, when, length of arc is 2×p×13, angle subtended is 2pie.
So, angle subtended when length of arc is 10pie
= 2pie/26pie × 10pie = 10pie/13.