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Regular polygon: number of sides from an angle fact, then diagonals n(n - 3)/2

This type of question, asked 3 times: 3 Mar 2023 Tier II, 6 Mar 2023 Tier II, 7 Mar 2023 Tier II. All 3 questions below, oldest first.

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  1. Question 1

    3 Mar 2023 Tier II

    16
    If the external angle of a regular polygon is 18∘18^\circ, then the number of diagonals in this polygon is:

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  2. Question 2

    6 Mar 2023 Tier II

    12
    Find the number of diagonals of a regular polygon, sum of whose interior angles is 2700∘2700^\circ.

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  3. Question 3

    7 Mar 2023 Tier II

    13
    If one of the interior angles of a regular polygon is 1516\frac{15}{16} times of one of the interior angles of a regular decagon, then find the number of diagonals of the polygon.

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