Question

In the above figure $\Delta$ ABD $\cong$ $\Delta$ ACD,If $\angle$BDC = ${110}^0$ and $\angle$DAC = ${30}^0$ then the measure of angle DBA is:

• A. ${70}^0$
• B. ${30}^0$
• C. ${40}^0$
• D. ${25}^0$

Answer 1

Answer: (D)

$\Delta$ ABD $\cong$ $\Delta$ ACD, $\angle$BDC = ${110}^0$ and $\angle$DAC = ${30}^0$

$\therefore$ $\angle DAB={30}^o$

$\because$ $\Delta$ ABD $\cong$ $\Delta$ ACD

$\therefore$ $\angle BDA=\angle CDA$ and $\angle BDA+\angle CDA={250}^o$

$⟹$ $\angle BDA=\angle CDA={125}^o$

We know that $\angle DAB+\angle DBA+\angle BDA={180}^o$

$\therefore$ $30+\angle DBA+125={180}^o$

$⟹$ $\angle DBA={25}^o$