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.
Solution:
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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