Q. 124.1( 10 Votes )

The diagonals AC A. 24°

B. 86°

C. 38°

D. 32°

Answer :

Given: ∠AOB = 70°

∠DAC = 32°

∵ AD ∥ BC and AC is transversal

∴ ∠ACB = 32°

Now,

∠AOB + ∠BOC = 180°

⇒ 70° + ∠BOC = 180°

⇒ ∠BOC = 180° - 70°

⇒ ∠BOC = 110°

Sum of all angles of a triangle = 180°

⇒ ∠BOC + ∠BCO + ∠OBC = 180°

⇒ 110° + 32°+ ∠OBC = 180°

⇒ 142°+ ∠OBC = 180°

⇒ ∠OBC = 180° - 142°

⇒ ∠OBC = 38°

Hence, ∠DBC = 38°

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The diagonals AC A. 24°B. 86°C. 38°D. 32°