If the measures of three of a quadrilateral are `(pi)/(3),(5pi)/(6) "and" 90^(@)` respectively, determine the sexagesimal and circular value of fourth angle.

Explanation

We have , `90^(@)=90^(@)xx(pi)/(180^(@))=(pi)/(2).`
Math (X)-38
Also, we that the sum of the four angles of a quadrilateral is `360^(@)=2xx 180^(@)=2pi.`
`therefore "fourth angle" =2pi-(2pi+5pi+3pi)/(3)=2pi-((pi)/(3)+(5pi)/(6)+(pi)/(2))`
`=2pi-(2pi+5pi+3pi)/(6)=2pi-(5pi)/(3)`
`=(6pi-5pi)/(3)=(pi)/(3).`
Also,`(pi)/(3)=(180^(@))/(3)=60^(@).`