Question 1138270
The arc length of a circle is {{{l=18pi}}} and the radius of the same circle is {{{36cm}}}. 

How big is the central angle that subtends the arc? 

{{{l=2pi*r(alpha/360)}}}

{{{18pi=2pi*36(alpha/360)}}}

{{{18pi/(72pi)=(alpha/360)}}}

{{{1/4=alpha/360}}}..... both sides multiply by {{{360}}}

{{{360/4=alpha}}}

{{{alpha=90}}}


or this way: 
The arc length of a circle is {{{l=18pi}}} which is a portion of the circumference {{{C=2rpi}}}

if the radius of the same circle is {{{36cm}}},{{{ 2rpi=2*36pi=72pi}}}

find ratio {{{l/C=18pi/72pi=1/4}}}=> central angle is {{{1/4}}} of full angle which is {{{360/4=90}}} degrees