Question

In the given figure, $\Delta ABD\cong \Delta ACD$. If $\angle BDC={110}^{\circ }$ and $\angle DAC={30}^{\circ }$, then the measure of $\angle DBA$ is :

• A. ${70}^{\circ }$
• B. ${40}^{\circ }$
• C. ${30}^{\circ }$
• D. ${25}^{\circ }$

Answer 1

The correct option is D ${25}^{\circ }$

$\Delta ABD\cong \Delta ACD$ (given)
$\therefore \angle DAC=\angle DAB={30}^{\circ }$ (By CPCT)
Also, $\angle ADC=\angle ADB=x$ (By CPCT)
Now, $\angle ADC+\angle ADB+\angle BDC=360$
$\Rightarrow x+x+110=360$ ...Angles at a point
$\Rightarrow x=125$
$\Rightarrow \angle ADC=\angle ADB={125}^{\circ }$
In $△ADB$
$\angle ADB+\angle BAD+\angle DBA={180}^{\circ }$ (Angles of a triangle)
$\Rightarrow {125}^{\circ }+{30}^{\circ }+\angle DBA={180}^{\circ }$
$\Rightarrow \angle DBA={180}^{\circ }-{155}^{\circ }={25}^{\circ }$
Hence, option 'D' is correct.