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

$x = 56 °, y = 76^{\circ}$

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

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

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

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Solution

The correct option is B
$x = 48^{\circ}, y = 56^{\circ}$

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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(\frac{- 3}{14} x y^{4}) \times (\frac{7}{6} x^{3} y)

\frac{3}{7} \times (\frac{5}{6} + \frac{12}{13}) = (\frac{3}{7} \times \frac{5}{6}) + (\frac{3}{7} \times \frac{12}{13})

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\frac{- 16}{7} \times (\frac{- 8}{9} + \frac{- 7}{6}) = (\frac{- 16}{7} \times \frac{- 8}{9}) + (\frac{- 16}{7} \times \frac{- 7}{6})

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