Question

If DB is the bisector of $\angle ADC?$, then which of the following options is/are correct?

• A. $\angle ADB=\angle BDC$
• B. $\angle ADB+\angle BDC=\angle ADC$
• C. $\angle ADC=2\times \angle ADB$
• D. $\angle ADC=2\times \angle BDC$

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A $\angle ADB=\angle BDC$
B $\angle ADB+\angle BDC=\angle ADC$
C $\angle ADC=2\times \angle ADB$
D $\angle ADC=2\times \angle BDC$

$\angle ADB=\angle BDC$
$\text{as BD is the angular bisector of}\angle ADC$
$Let\angle ADB=\angle BDC=x\therefore \angle ADC=\angle ADB+\angle BDC=2x\Rightarrow \angle ADC=2x=2\angle ADB=2\angle BDC$