Question : If in a $\triangle$ABC as drawn in the figure, AB = AC and $\angle$ACD = 130°, then $\angle$BAC is equal to:
Option 1: 60°
Option 2: 50°
Option 3: 70°
Option 4: 80°
Correct Answer: 80°
Solution :
$\angle$ACD = 130°
Now, $\angle$ACD + $\angle$ACB = 180°
⇒ 130° + $\angle$ACB = 180°
⇒ $\angle$ACB = 180° – 130° = 50°
Since AB = AC,
⇒ $\angle$ABC = $\angle$ACB = 50°
We know that $\angle$ABC + $\angle$ACB + $\angle$BAC = 180°
⇒ 50° + 50° + $\angle$BAC =180°
⇒ $\angle$BAC = 180° – 100° = 80°
Hence, the correct answer is 80°.
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