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the number of sides in 2 regular polygons is in the ratio 5:4 an the difference between their angles is 9^o. Find the number of sides in the polygon

  • Geometry -

    The internal angle each corner of a regular polygon is 180 - 360/n degrees.

    Let N be the number of sides of polygon with fewer sides. The other polygon then has 5N/4 sides.

    180 - 360/N - [180 - 360*0.8/N] = -9
    -360/N + 288/N = -9
    72/N = 9
    N = 8
    The other polygon has 10 sides.
    The internal angles are 135 and 144 degrees.

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