Problem
GEO-B1-M01-P010 An Angle Bisector in a Triangle
#10
★★☆☆☆ Level 2 of 5
In triangle \(ABC\), \(\angle B=42^\circ\), \(\angle C=74^\circ\). The angle bisector of angle \(A\) meets side \(BC\) at \(D\). Find \(\angle BDA\) and \(\angle ADC\).
First find \(\angle A\), then half of it.
We have \(\angle A=180^\circ-42^\circ-74^\circ=64^\circ\). Since \(AD\) is the angle bisector, \(\angle BAD=32^\circ\). In triangle \(ABD\), \(\angle BDA=180^\circ-42^\circ-32^\circ=106^\circ\). Hence \(\angle ADC=180^\circ-106^\circ=74^\circ\).
This problem teaches students to distinguish \(BDA\) and \(ADC\) carefully.