QuestionAn isosceles triangle ABC, with AB = AC, is split into three smaller isosceles triangles, as shown, so that AD= DB, CE= CD, and BE= EC. (Note that the diagram is not drawn to scale.) What is the size, in degrees, of angle BAC? |
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| A: 24 | B: 28 | C: 30 | D: 35 | E: 36 |
LLM Response: Since triangle ABC is an isosceles triangle with AB = AC, we know that angle BAC is equal to either angle ABC or angle ACB. Since the diagram also shows that triangle ADE and triangle CEF are both isosceles, we can conclude that triangle ABC has angles of 72 degrees at each vertex (since the sum of the angles in a triangle is 180 degrees). Therefore, angle BAC is also 72 degrees. So the answer is \boxed{C3}.
Final Prediction: Puzzle #89: Solve this question with explanation of the intermediate steps. Your response must end with one of the selected answer options from A1, B2, C3, D4, or E5. An isosceles triangle ABC, with AB = AC, is split into three smaller isosceles triangles, as shown, so that AD= DB, CE= CD, and BE= EC. (Note that the diagram is not drawn to scale.) What is the size, in degrees, of angle BAC? Options: A1: 24, B2: 28, C3: 30, D4: 35, E5: 36. Predicted Answer = C Correct Answer = E