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In the adjoining figure ,O is the center...

In the adjoining figure ,O is the center of the circle and AB is a diameter. If `angleAOD=140^(@)andangleCAB=50^(@)`, then find value of `angleBED`

Text Solution

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Given that `angleAOD=140^(@)`
`therefore"reflex "angleAOD=360^(@)-140^(@)=220^(@)`
Again , the central angle produced by the are `overset(frown)(ABD)` is reflex `angleAOD` and angle in circle = `angleACD`
`therefore" reflex "angleAOD=2angleACD`
or, `220^(@)=2angleACD"or "angleACD=(220^(@))/(2)=110^(@)`
Given that `angleCAB=50^(@)`
Now ,in `DeltaACE,angleAEC+angleEAC+angleACE=180^(@)"or, "angleAEC=180^(@)-50^(@)-110^(@)=20^(@)`
Hence `angleBED=20^(@)`
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