Question

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

• 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 1

The correct option is B

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

Consider $△ABC$ and $△ADC$



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

$\therefore △ABC\cong △CDA$ ... (SSS Postulate)

$\Rightarrow \angle ABC=\angle CDA$ ..... (CPCT)

$\therefore x={48}^{\circ }$

$\Rightarrow \angle BCA=\angle DAC$ ......(CPCT)

$\therefore y={56}^{\circ }$