ABCD is a quadrilateral in which angle BAD =105, angel BCD =150 and BC= 13cm . find AC? please solve this question​

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1. Answer:

   (i) Join BD

   Now, ABCD is a cyclic quadrilateral

   ∴ ∠BAD + ∠BCD = 180° (Opposite angles of a cyclic quadrilateral)

   => ∠BAD + 150° = 180°

   => ∠BAD = 180° – 150° = 30°

   (ii) ∠ABD = 90° (Angle in a semi-circle)

   Now, In △ABD, we have

   ∠ABD + ∠BAD + ∠ADB = 180°

   90° + 30° + ∠ADB = 180°

   => ∠ADB = 180° – 120° = 60°

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