Question

if ABC is an arc of a circle and angle ABC= 135
then the ratio of arc abc to circumference?

Answer 1

Now, if my figure is correct, ABC is the arc with m<ABC = 135

Let O be the center of the circle.

Also, let arc ABC subtend angle APB in other segment of circle.

Now, Quadrilateral ABCP forms cyclic quadrilateral.

So, m<ABC + m<ABP  = 180
So, 135 + m<ABP = 180
So,  m<ABP = 180 - 135 = 45

So, m<AOB = 2 X m<APB = 2 X 45 = 90

Now, length of arc(L)  =  πr² X m<AOB      ( r =radius of circle)
                                         180 

So,   L   =   r X 90
      πr         180

So,    L   =    r  
       πr        2

So,      L      =   r  
        2πr          4