SSC CGL 2012 Tier 1 1 July NZ Morning III

Question 123

In ΔABC, AD is the median and AD = 1/2 BC. If ∠BAD = 30°, then measure of ∠ACB is

Solution

Consider , a triangle ABC . AD is the median .So, BD=DC. also given that AD = 1/2 BC.
So AD=DC .This makes ΔADC & ΔABD as isosceles triangles.
So , ∠BAD = ∠ABD = 30. Hence , ∠ADB = 180 - 30 - 30 = 120 . So, ∠ADC = 60.
Now, in ΔADC , ∠C=∠A .
Hence, ∠C + 60 + ∠A = 180 .
2∠C = 120 .
∠C = 60











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