Discussion

In \(\triangle ABC\), \(\angle B = 90°\). The bisector of \(\angle A\) meets BC at D. If \(\angle C = 30°\), find the measure of \(\angle ADC\).

Answer: A

Correct answer: 120°

First, \(\angle A = 180° - 90° - 30° = 60°\), and AD bisects it, so \(\angle BAD = \angle DAC = 30°\).

In \(\triangle ABD\) the angles at B and A are \(90°\) and \(30°\), so \(\angle ADB = 60°\). As D lies on BC, \(\angle ADC\) is its supplement:

\[\angle ADC = 180° - 60° = 120°\]

Checking against \(\triangle ADC\) directly: its angles \(\angle DAC = 30°\) and \(\angle C = 30°\) leave \(\angle ADC = 120°\).

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