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°
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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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