Question

# In the given figure, AD divides ∠BAC in the ratio 1:3. Find the value of X and ∠ADC (in degrees).

A

20, 115

B

115, 20

C

30, 125

D

20, 125

Solution

## The correct option is A 20, 115 ∠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∘

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