Question

$\text{Find the value of}\angle ABD\text{from the figure?}$

• A. ${45}^{\circ }$
• B. ${40}^{\circ }$
• C. ${50}^{\circ }$
• D. ${90}^{\circ }$

Answer 1

The correct option is B ${40}^{\circ }$


$\text{In the given figure,}\angle ABC=\angle BDC={90}^o\Rightarrow \angle ADB={90}^o$

$\text{Hence,}△ABC,△BDC\text{and}△ABD\text{are right angled triangles.}$

$\text{In}△ABC,\text{by angle sum property,}\angle ABC+\angle BCA+\angle CAB={180}^o{90}^o+{40}^o+x={180}^{o}x={180}^o-{130}^o={50}^o$
$\text{In,}△BDA,\angle ADB={90}^o,\angle DAB={50}^o$

$\text{By angle sum property,}\angle ABD+\angle BDA+\angle DAB={180}^o\angle ABD+{90}^o+{50}^o={180}^o\angle ABD={180}^o-{140}^o={40}^o$

$\text{Hence, the value of}\angle ABD={40}^o.$