In the adjoining figure, ABCD is a square. A line segment CX cuts AB at X and the diagonal BD


In the adjoining figure, ABCD is a square. A line segment CX cuts AB at X and the diagonal BD at O such that COD = 80° and ∠OXA = x°. Find the value of x.



The angles of a square are bisected by the diagonals.
∴ ∠​OBX = 45o                        [∠​ABC = 90o and BD bisects ∠​ABC​]
And ∠​BOX = ∠COD = 80o           [Vertically opposite angles]
∴​ In ∆BOX, we have:
∠AXO = ∠OBX + ​∠BOX        [Exterior angle of ∆BOX]
⇒​ ∠AXO = 45o + 80o = 125o
∴ ​x =125o

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