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Angles and Its Components

In the given ...

Question

In the given figure, $∠$ DAB = $∠$ CBA and AD = BC. Then which angle is equal to $∠$ ACD?

$∠$ BCD

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$∠$ BDC

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$∠$ CAD

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$∠$ DBC

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Solution

The correct option is B
$∠$ BDC

In triangle ADB and triangle BCA,

$∠$ DAB = $∠$ CBA [Given]
AD = BC [Given]
AB = AB [Common side]

$∴$ $△ A D B ≅ △ B C A$

Therefore, from the properties of congruent triangles, $∠ A C D = ∠ B D C$

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