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Two regular polygons, one from its interior-angle sum and one from an angle condition: sum of their numbers of sides

This type of question, asked 2 times: 29 Jan 2022 Tier II, 3 Feb 2022 Tier II. All 2 questions below, oldest first.

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  1. Question 1

    29 Jan 2022 Tier II

    41
    The sum of the interior angles of a regular polygon A is 1260 degrees and each interior angle of a regular polygon B is 12847128\frac{4}{7} degrees. The sum of the number of sides of polygons A and B is:

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  2. Question 2

    3 Feb 2022 Tier II

    11
    A1A_1 and A2A_2 are two regular polygons. The sum of all the interior angles of A1A_1 is 1080∘1080^\circ. Each interior angle of A2A_2 exceeds its exterior angle by 132∘132^\circ. The sum of the number of sides A1A_1 and A2A_2 is:

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