Question : If in a $\triangle ABC$, $\angle ABC=5\angle ACB$ and $\angle BAC=3\angle ACB$, then what is the value of $\angle ABC$?
Option 1: $130°$
Option 2: $80°$
Option 3: $100°$
Option 4: $120°$
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Correct Answer: $100°$
Solution :
Given:
$\angle ABC$ = $5\angle ACB$
$\angle BAC$ = $3\angle ACB$
Now, $\angle ABC+\angle ACB+\angle BAC$ = $180^{\circ}$
⇒ $5\angle ACB+\angle ACB+3\angle ACB$ = $180^{\circ}$
⇒ $9\angle ACB=180^{\circ}$
⇒ $\angle ACB=20^{\circ}$
⇒ $\angle ABC =5\times20^{\circ} =100^{\circ}$
Hence, the correct answer is $100^{\circ}$.
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