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In the Given Figure Ac is a Tangent to the Circle with Centre O. If ∠Adb = 55° , Find X and Y. Give Reasons for Your Answers. - Mathematics

Sum

In the given figure AC is a tangent to the circle with centre O.
If  ∠ADB = 55° , find x and y. Give reasons for your answers. 

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Solution

In ΔABD, ∠BAD = 90°
∴ ∠ABD + ∠BAD + ∠ADB = 180°         {Sum of angles in a triangle}
∴ ∠ABD + 90°  + 55°  =180°  
∴ ∠ABD = 35°  
Also ∠AOE = 2∠ABE = 2∠ABD

∴ ∠AOE = y = 2 × 35° 

y = 70° 

 

In  Δ AOC,
∠OAC + x + y = 180°
∴ 90° + x + 70° = 180°
∴  90° + x + 70° = 180°

⇒ x = 20°
  Is there an error in this question or solution?
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