Select the statements that are true.

$∠ C D B = 49^{\circ}$

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$∠ A B C = 43^{\circ}$

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$∠ A C B = 88^{\circ}$

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$∠ A C B = 28^{\circ}$

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Solution

The correct options are
A
$∠ C D B = 49^{\circ}$

B
$∠ A B C = 43^{\circ}$

C
$∠ A C B = 88^{\circ}$

$∠ C D B = ∠ B A C$ (Angles is the same segment) = $49^{\circ}$

$∠ A B C = ∠ A D C$ (Angles in the same segment) = $43^{\circ}$

$∴ ∠ A D B = ∠ A D C + ∠ B D C = 43^{\circ} + 49^{\circ} = 92^{\circ}$ and $∠ A D B + ∠ A C B = 180^{\circ}$

(opposite angles of a cyclic quad)

$∴ ∠ A C B = 180^{\circ} - ∠ A D B$

$= 180^{\circ} - 92^{\circ} = 88^{\circ}$

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