Question : ABC is an isosceles triangle such that AB = AC, $\angle$ABC = 55°, and AD is the median to the base BC. Find the measure of $\angle$BAD.
Option 1: 50°
Option 2: 55°
Option 3: 35°
Option 4: 90°
Correct Answer: 35°
Solution :
Given, ABC is an isosceles triangle with AB = AC
$\angle$ ABC = 55°
AD is the median to the base BC which bisects $\angle$BAC
By angle sum property in $\triangle$ABC,
$\angle$BAC + $\angle$ABC + $\angle$ACB = 180°
or, $\angle$BAC + 55° + 55° = 180°
or, $\angle$ BAC = 70°
So, $\angle$BAD = $\angle$CAD = $\frac{1}{2}\angle$BAC
or, $\angle$BAD= 35°
Hence, the correct answer is 35°.
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