Two lines A B\ a n d\ C D intersect at O...

Two lines `A B\ a n d\ C D` intersect at `Odot` If `/_A O C+/_C O B+/_B O D=270^0` , find the measures of `/_A O C ,\ /_C O B ,\ /_B O D` and `/_D O A`.

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Solution
Let '/_AOC=x and /_COB=y'.
Then, '/_BOD=x' and /_DOA=y'
Now, '/_AOC+ /_COB+/_BOD=270 @'
⇒'x+y +x=270@'
⇒'2x +y = 270@'
But, 'x+y=180@'
∴'x=y=90@'

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