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The value of x is 125°
Step-by-step explanation:
Let, B is meeting at E on CD.
∠BCD = 90° [∵ Angles of a square measure 90°.]
It is given that, AC is the diagonal of the square ABCD.
Hence,
∠ ACD = 1/2 ∠BCD [∵ Diagonals of a square bisect the angles on which they are being produced.
∴ ∠ACD = (90*1/2)
= 45°
∠COE = ∠AOB = 80° [∵ Vertically opposite angles.]
For triangle COE _
∠COE = 80°
∠OCE = 45°
∠CEO = ?
We know that,
∠CEO + ∠COE + ∠OCE = 180° [∵Angle sum property]
⇒ ∠CEO + 80°+45° = 180°
⇒ ∠CEO + 125° = 180°
⇒ ∠CEO = 180° - 125°
⇒ ∠CEO = 55°
∠CEO + ∠OED = 180° [∵Linear pair.]
⇒ 55° + x = 180°
⇒ x = 180° - 55°
⇒ x = 125°
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