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MathNet 2016-part-03 — 184 problems (EN–VI) Question 172

Math Olympiad Vault · MathNet 2016-part-03 — 184 problems (EN–VI)

Question 172

In an acute triangle, three of the adjacent angles around the orthocenter, made by the altitudes, have their measures directly proportional with $5$, $5$ and $7$, and the sum of the other three angles is $190^\circ$. Find the measure of the angles of the triangle.
Constantin Apostol