In the given figure lines AB and CD intersect at O. If Ð BOC + Ð BOE = 70⁰ and Ð BOD = 130⁰, find ഋOC and reflex Ð AOC

 
Lines AB and CD intersect at O
∴ ∠ AOC = ∠ BOD                          | Vertically Opposite Angles
But ∠ BOD = 130° …(1)                    | Given 
∴ ∠ AOC = 130° ….(2)
Now, ∠ AOC + ∠ COB = 180°                     | Linear Pair Axiom
⇒ 130⁰ + ∠ COB = 180⁰                   |Using (2)         Þ  ∠ COB   = 50⁰     
Again, Reflex ∠ AOC = ∠ COB + ∠ BOA 
                          = 50⁰  +180° ........(3)     Since,  ∠ BOA =∠ BOD +∠ AOD = 180°   (Linear Pair Axiom)
                          = 230°