Using the information given in the figure, the values of x and y are ___________

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Using the information given in the figure, the values of x and y are ___________.

Options:

A .

x = 56 °, y = 76^{\circ}

B .

x = 48^{\circ}, y = 56^{\circ}

C .

x = 48^{\circ}, y = 76^{\circ}

D .

x = 76^{\circ}, y = 56^{\circ}

Answer: Option B
:
B

Consider $△ A B C$ and $△ A D C$

(i) AB = CD ...... (given)
(ii) BC = DA ...... (given)
(iii) AC = AC ...... (common)

$∴ △ A B C ≅ △ C D A$ ... (SSS Postulate)

$\Rightarrow ∠ A B C = ∠ C D A$ ..... (CPCT)

$∴ x = 48^{\circ}$

$\Rightarrow ∠ B C A = ∠ D A C$ ......(CPCT)

$∴ y = 56^{\circ}$

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