Question 17
A convex heptagon is given. Choose any four of its angles and take their sines; take the cosines of the remaining three angles. The sum of these seven numbers does not depend on the original choice of four angles. Prove that four angles of the heptagon are equal.
Schematic convex heptagon (the equal-sum hypothesis is not encoded by the drawing).
Schematic convex heptagon (the equal-sum hypothesis is not encoded by the drawing).