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MathNet 2018-part-02 — 181 problems (EN–VI) Question 105

Math Olympiad Vault · MathNet 2018-part-02 — 181 problems (EN–VI)

Question 105

Teacher drew a pentagon on the blackboard. The following conditions hold for the pentagon.

a) Two of the pentagon's interior angles are equal.

b) There exist three interior angles such that the first one equals the sum of the other two.

c) There exist four interior angles such that one of them equals the sum of the other three.

d) There exists an interior angle that equals the sum of the other four.

Find the interior angles of the pentagon.