In an equilateral triangle each interior angle is trisected by a pair of rays. The intersection of the interiors of the middle 20°-angle at each vertex is the interior of a convex hexagon. What is the degree measure of the smallest angle of this hexagon?
$$\textbf{(A) } 80 \qquad \textbf{(B) } 90 \qquad \textbf{(C) } 100 \qquad \textbf{(D) } 110 \qquad \textbf{(E) } 120$$
Difficulty: 28/100 — Drawing precise diagram helps; then computation is easy. Intimidating for many contestants.
Core Concepts: angle chasing, equilateral triangles
Challenges: Recognizing that the hexagon is formed by the angles of an isosceles triangle. Drawing an accurate diagram.
Techniques: Focus on one triangle at a time; use angle sum and vertical angles.
Error-prone Steps: Assuming hexagon is equiangular (leads to 120°).
Ideal Time:
Experienced: ≤ 25 sec
Intermediate: ≤ 1 min
Beginner: ≤ 2 min