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In the figure , points G,D,E,F are concy...

In the figure , points G,D,E,F are concyclic points of a cicle with centreC.
`/_ECF = 70^(@)`
m ( arc DGF ) `= 200^(@)`,
find m(arc DE) and m(arc DEF ) .

Text Solution

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The correct Answer is:
`:. m(arc DE) =90^(@)` and `m(arc DEF) =160^(@)`
`m(arc EF)=/_ECF " " "….."(" Definition of measure of minor arc " )`
`/_ECF=70^(@)" " "……."(" Given ")`
`:. M (arc EF)=70^(@)`
`m(arc DGF) +m(arc EF)+m(arcDE)=360^(@)`
`" " "……"(" Measure of a circke is " 360^(@))`
`:. 200^(@)+70^(@)+m(arcDE)=360^(@)`
`:. 270^(@)+m(arc DE)=360^(@)`
`:. m(arc DE)=360^(@)=270^(@)`
`:. m(arc DE)=90^(@)`
`m(arc DE)+m(arcEF)=m(arc DEF) " " "......"(" Arc addition postulate ")`
`:.90^(@)+70^(@)=m(arc DEF)`
`:. m(arc DEF) =160^(@)`
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