ABCD is a square.A line segment CX cuts AB at X and the diagonal BD at O, such that angle COD=80° and angle OXA=x° . Find the value of x°
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Step-by-step explanation:
=> According to the question, ABCD is a square. and a line segment CX cuts AB at X and the diagonal BD at O, such that ∠COD=80°.
But, diagonal of a square also bisects their angles.
∴ ∠ADB = ∠ABD = 45°
=> Here, ∠COD and ∠XOD are supplementary angles.
∴ ∠COD + ∠XOD = 180°
80° + ∠XOD = 180° [ ∵ ∠COD = 80°]
∠XOD = 180° - 80°
∠XOD = 100°
=> Suppose, AXOD is the quadrilateral. so the sum of its angles is:
∠AXO + ∠XOD + ∠ADO + ∠XAD = 360°
x + 100° + 45° + 90° = 360°
x + 235° = 360°
x = 360° - 235°
x = 125°
Therefore, the value of x is 125°.
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