Question

If the perimeter of a sector is 4 times its radius, then the radian measure of the central angle of the sector is

Answer 1

We  know that

the perimeter of a circumference=2*pi*r

If the perimeter of a sector is 4 times its radius, then the arc measure of the sector is (4r-2r)----> 2r
so
if 2*pi radians (full circle) has a length------------------> 2*pi*r
 X radians -------------------------------------------> 2*r  (the sector)
X=2*r*(2*pi)/(2*pi*r)-----> x=2

the answer is
2