Question

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.

Answer 1

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