ISEE Upper Level Quantitative Reasoning Question of the Day

1. 71° (correct answer)
2. 76°
3. 81°
4. 86°

Explanation: When you encounter isosceles triangles, remember that they have two equal sides and two equal angles (called base angles). The key insight is that all triangles have interior angles that sum to exactly 180°. In this problem, you're given that the vertex angle (the angle between the two equal sides) measures 38°. Since the two base angles are equal in an isosceles triangle, you can call each base angle $x$. Setting up the equation: $38° + x + x = 180°$, which simplifies to $38° + 2x = 180°$. Solving for $x$: $2x = 180° - 38° = 142°$, so $x = 71°$. Each base angle measures 71°. Looking at the wrong answers: Choice B (76°) would give you a triangle with angles of 38° + 76° + 76° = 190°, which exceeds 180° and is impossible. Choice C (81°) would result in 38° + 81° + 81° = 200°, also impossible. Choice D (86°) would create 38° + 86° + 86° = 210°, far exceeding the required sum. These incorrect options likely represent common calculation errors or the misconception that you might use different formulas for isosceles triangles. The answer is A (71°). Strategy tip: For any isosceles triangle problem, immediately identify which angle is given (vertex or base), set up the equation using the fact that angles sum to 180°, and remember that the two base angles are always equal. This systematic approach prevents calculation mistakes.