Question

In the given figure, $AB=DB$ and $AC=DC$. If $\angle ABD={58}^{\circ }$,

$\angle DBC=(2x-4{)}^{\circ }$, $\angle ACB=y+{15}^{\circ }$ and
$\angle DCB={63}^{\circ }$, find the values of $x$ and $y$

• A. $x=(16.5{)}^{\circ }andy={48}^{\circ }$
• B. $y=(16.5{)}^{\circ }andx={48}^{\circ }$
• C. $x=(16.5{)}^{\circ }andy=(16.5{)}^{\circ }$
• D. $x={48}^{\circ }andy={48}^{\circ }$

Answer 1

The correct option is A $x=(16.5{)}^{\circ }andy={48}^{\circ }$

In $△ABC$ and $△DBC$

$AB=BD$ ...(Given)
$AC=CD$ ...(Given)

$AC=AC$ ...(Common)
Thus, $△ABC\cong △DBC$ ...(SSS rule)

Hence, $\angle DBC=\angle ABC$ ...(By CPCT)
$\angle DBC=\frac{1}{2}\angle ABD$

$2x-4=29$
$x={16.5}^{\circ }$
Also, $\angle ACB=\angle DCB$ ...(By cpct)

$y+15=63$
$y={48}^{\circ }$