Question

In the given figure, AD divides $\angle BAC$ in the ratio 1:3. Find the value of X and $\angle ADC$ (in degrees).

• A. 20${}^{\circ }$, 115${}^{\circ }$
• B. 115${}^{\circ }$, 20${}^{\circ }$
• C. 30${}^{\circ }$, 125${}^{\circ }$
• D. 20${}^{\circ }$, 125${}^{\circ }$

Answer 1

The correct option is A

20${}^{\circ }$, 115${}^{\circ }$

$\angle EAC=\angle ABC+X$ (external angle property)
${120}^{\circ }={100}^{\circ }+X$
So, $X={20}^{\circ }$

$\angle BAC+\angle ACB+\angle ABC={180}^{\circ }$
$\angle BAC+X+{100}^{\circ }={180}^{\circ }$
Hence, $\angle BAC={60}^{\circ }$
Therefore, $\angle DAC=\frac{3}{4}\angle BAC={45}^{\circ }$ ( because 1 and 3 are in ratio 1:3)

$\angle ADC={180}^{\circ }-({45}^{\circ }+20)={115}^{\circ }$