Question

Find $x$ in the figure:

(ii) Given $DA=DB=DC,BD$ bisects $\angle ABC\text{and}\angle ADB={70}^{\circ }$

Answer 1

Find the equal angles in given isosceles triangle

Given :$DA=DB=DC,BD$ bisects $\angle ABC\text{and}\angle ADB={70}^{\circ }$

$\because DA=DB$
$\Rightarrow \angle DBA=\angle DAB$
Since, $\angle ADB+\angle DAB+\angle DBA={180}^{\circ }$
[$\because$ Angle sum property of triangle ]
${70}^{\circ }+\angle DBA+\angle DBA={180}^{\circ }$
$2\angle DBA={180}^{\circ }-{70}^{\circ }$
$2\angle DBA={110}^{\circ }$

$\angle DBA=\frac{{110}^{\circ }}{2}$
$\therefore \angle DBA={55}^{\circ }$
Find $x$:
As, $BD$ is the bisector of $\angle ABC$
$\therefore \angle DBA=\angle DBC={55}^{\circ }$
In $\Delta DBC,DB={55}^{\circ }$
$\therefore x=\angle DBC={55}^{\circ }$
Hence, the value of $x$ is ${55}^{\circ }$.