Let OA, OB, OC and OD be rays in anticlockwise direction starting from OA such (( hkp szdt pdj )) that ZAOB = ZCOD= 100°, ZBOC = 82° and ZAOD = 78°. Is it true that AOC and BOD are straight lines? Justify [CBSE SP 2012] your answer. make a diagram using the following information
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Answer:Given, OA, OB, OC and OD are rays in the anticlockwise direction.
∠ AOB = ∠COD = 100°
∠BOC = 82°
∠AOD = 78°
If AOC is a line the linear pair of angles must be equal to 180°
So, ∠AOB + ∠COB = ∠AOC
∠AOC = 110° + 82°
∠AOC = 192°
∠AOC is not equal to 180°
Therefore, AOC is not a line.
Similarly, ∠BOC + ∠COD = ∠BOD
∠BOD = 82° + 100°
∠BOD = 182°
∠BOD is not equal to 180°
Therefore, BOD is not a line.
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