2025 AMC 10 A

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Problem 6 Easy

In an equilateral triangle each interior angle is trisected by a pair of rays. The intersection of the interiors of the middle 2 0 ^ { \circ }-angle at each vertex is the interior of a convex hexagon. What is the degree measure of the smallest angle of this hexagon?

  • A.

    80

  • B.

    90

  • C.

    100

  • D.

    110

  • E.

    120

Answer:C

 

Computing the angles: \angle 1 = 180^\circ - 40^\circ - 40^\circ = 100^\circ \angle 2 = 180^\circ - 20^\circ - 20^\circ = 140^\circ

By symmetry, the hexagon's six angles are 100^\circ, 100^\circ, 100^\circ, 140^\circ, 140^\circ, 140^\circ.

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