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The side BC of a triangle ABC is extended to D. If ∠ ACD = 120° and ∠ ABC = ( 1/2 )∠ CAB, then the value of ∠ ABC is
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- 80°
- 40°
- 60°
- 20°
- 80°
Correct Option: B
Firstly , we draw a figure triangle ABC whose the side BC is extended to D , 
According to given question.
∠ CAB = 2 ∠ ABC
∠ ACB + ∠ ACD = 180°
⇒ ∠ ACB + 120° = 180° { ∴ ∠ ACD = 120° }
⇒ ∠ ACB = 180° – 120° = 60°
∴ ∠A + ∠B = 180° – 60° = 120°
⇒ 2∠B + ∠B = 120°
⇒ 3∠B = 120°
⇒ ∠B = 120° ÷ 3 = 40°
