Question

In triangle ABC, let D be the midpoint of BC. If angle ADB is equal 45 and angle ACD is equal 30. Calculate angle BAD.

Answer 1

given:  D is midpoint of BC, angle ADB = 45, angle ACD = 30

to find: angle BAD

1. in triangle ABC, AD bisects angle A,

• ∠ADB + ∠ADC = 180°  
• (linear pair)

• 45 + ∠ADC = 180°

• ∠ADC = 135°

2. now, in triangle ADC,

• ∠A +∠D +∠C = 180°  
• (angle sum property of a triangle)

• ∠A + 135° + 30° = 180°

• ∠DAC = 15°

So ∠DAC = 15°  (since both angles are same as angle bisector)

∴ ∠BAD = DAC = 15° ∵angle bisector theorem

Answer 2

Step-by-step explanation:

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