Multiple choice

ABC is an isosceles triangle such that AB=AC,∠ABC=55∘ and AD is the median to the base BC. Find the measure of ∠BAD.

  1. 50∘

  2. 55∘

  3. 35∘

  4. 90∘
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C Correct answer
Explanation

Since triangle ABC is isosceles with AB=AC, the base angles ∠ABC and ∠ACB are equal. Given ∠ABC=55°, we have ∠ACB=55° and ∠BAC=180°-55°-55°=70°. In an isosceles triangle, the median to the base is also the angle bisector of the vertex angle, so AD bisects ∠BAC. Therefore, ∠BAD=70°/2=35°.

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