A cyclic polygon has n sides such that each of its interior angle measures `114^(@).` What is the measure of he angle subtended by each of its sides at the geometrical centre of the polygon?

Explanation

Each interior angle of n-sided polygon `=(n-2)/(n)xx180`
`therefore" "(n-2)/(n)xx180=144^(@)`
`implies" "(n-2)xx5=4n`
`implies" "5n-10=4n`
`implies" "n=10`
Let each central angle be `theta=(360)/(n)=(360)/(10)=36^(@)`