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Obtuse triangles in a regular 17-gon

Source: 2014-2015 SDML High School 1a Problem 13/2014-2015 SDML Middle School 1a Problem 15

August 28, 2016
2014-15 SDML Round 1SDML High SchoolSDML Middle School

Problem Statement

How many triangles formed by three vertices of a regular 1717-gon are obtuse?
(A) 156(B) 204(C) 357(D) 476(E) 524\text{(A) }156\qquad\text{(B) }204\qquad\text{(C) }357\qquad\text{(D) }476\qquad\text{(E) }524
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