In Figure, `A B C D` is quadrilateral inscribed in a circle with centre `OdotC D` is produced to `E` such that `/_A DE=95^0a n d\ /_O B A=30^0dot` Find `/_O A C`

Explanation

In the figure, `ABCD` is a cyclic quadrilateral
`CD` is produced to`E`
`/_ADE=95^0`
`O` is the center of the circle
`/_ADC+/_ADE=180^0`
`/_ADC+95^0=180^0`
`/_ADC=180^0-95^0=85^0`
Now are `ABC` subtends `/_AOC`
at the center
`/_ADC`
at the remaining part of the circle
`/_AOC=2/_ADC=2xx85^0=170^0`
Now in `/_\ OAC,/_OAC +/_OCA +/_\AOC=180^0`(sum of angles of a tringle)
`/_OAC=OCA`(OA =AC radii of the circle)
`/_OAC+/_OAC+170^0=180^0`
`2/_OAC=180^0-170^0=10^0`
`/_OAC=10/2=5^0`