In Figure, A O B is a straight line. If ...

In Figure, `A O B` is a straight line. If `/_A O C+/_B O D=85^0,` then `/_C O D=` (a)`85^0` (b) `90^0` (c) `95^0` (d) `100^0`

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SOLUTION
It is given that `AOB` is a straight line.
Also,`/_AOC, /_BOC, and /_COD` form a linear pair.
Therefore, their sum must be supplementary.
`/_AOC + /_BOD + /_COD = 180^@`
It is given that
`/_AOC + /_BOD = 85^@`
On substituting the value of (2) in (1) we get,
`/_COD +85^@ = 180^@`
`⇒ /_COD =180^@ - 85^@`
⇒`/_COD =95^@`.

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