In \(\triangle ABC\), D is a point on side BC such that \(\angle ADC=2\angle BAD\). If \(\angle A=70^\circ\) and \(\angle C=48^\circ\), what is the measure of \(\angle ADB\)?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 56°
\(\angle ADC\) is an exterior angle of \(\triangle ABD\), so it equals the sum of the two opposite interior angles, \(\angle B\) and \(\angle BAD\).
\(\angle B=180^\circ-70^\circ-48^\circ=62^\circ\)
Let \(\angle BAD=x\); then \(\angle ADC=2x\)
Exterior angle: \(2x=\angle B+x=62^\circ+x\), so \(x=62^\circ\)
\(\angle ADC=2\times62^\circ=124^\circ\)
\(\angle ADB=180^\circ-124^\circ=56^\circ\)
