In the given figure, AD divides ∠BAC in the ratio 1:3. Find the value of X and ∠ADC (in degrees).
∠EAC=∠ABC+X (External angle property)
120∘=100∘+X
So, X=20∘
∠BAC+∠ACB+∠ABC=180∘
∠BAC+X+100∘=180∘
Hence,
∠BAC=60∘
Therefore,
∠DAC=34∠BAC=45∘
(because 1 and 3 are in ratio 1:3)
∠ADC=180∘−(45∘+20)=115∘