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In triangle ABC, D is the midpoint of BC. Given angle ADB = 45 deg and angle ACD = 30 deg, find angle BAD.

1. 30 deg
2. 45 deg
3. 15 deg
4. 60 deg

Correct answer: 30 deg

Solution

Angle ADC = 180 - 45 = 135 deg. In triangle ADC: angle DAC = 180 - 135 - 30 = 15 deg. By sine rule in ADC: AD/sin30 = DC/sin15. In triangle ABD with angle ADB = 45 deg: AD/sin(B) = BD/sin(BAD). Using BD = DC and solving the ratio gives angle BAD = 30 deg.

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