Question

In given figure, $AB$ divides $\angle DAC$ in the ratio $1:3$ and $AB=DB$. Determine the value of $x$.

• A. ${62}^o$
• B. ${54}^o$
• C. ${90}^o$
• D. ${70}^o$

Answer 1

The correct option is B ${54}^o$

$\angle DAC=180°-108°=72°\frac{\angle BAC}{\angle DAB}=\frac{1}{3}$ Given

$\Rightarrow \angle DAB=3\angle BAC\therefore \angle BAC+\angle DAB=\angle DAC=72°\Rightarrow \angle BAC+3\angle BAC=72°\Rightarrow 4\angle BAC=72°\Rightarrow \angle BAC=\frac{72}{4}=18°\therefore \angle DAB=3\times 18°=54°\therefore \angle DAB=\angle BDA=54°(AB=DB)\therefore \angle ABD=180°-(54°+54°)=180-108°=72°$

No, $\angle DBA=72°=\angle BAC+x$ (Exterio angle)

$\Rightarrow x=72°-18°=54°$