• Angles in a polygon
    Find the Sum of all Interior & all Exterior Angle and Value of Each angle in a 4-sided polygon. Share to Whatsapp





  • There are 2 types of angles formed in a polygon at a vertex :
    Internal Angle : In geometry, an angle of a polygon is formed by two sides of the polygon that share an vertex. This angle is called an interior angle (or internal angle)
    The sum of the measures of the interior angles of a polygon with n sides is (n – 2) * 180.

    External Angle : In contrast, an exterior angle (or external angle) is an angle formed by one side of a simple polygon and a line extended from an adjacent side.
    The sum of the measures of the exterior angles of a polygon is always 360°.


  • We know that the sum of the angles in a n-sided polygon is always sum up to (n-2) × 180°
    Sum of Interior angles = (4-2) × 180°
    Sum of Interior angles = (2) × 180°
    Sum of Interior angles = 360°

    Sum of Exterior angles = 360°


    Let
    a = 74 °
    b = 106 °
    c = 70 °
    Thus a + b + c + d = 360°
    Thus d = 360° - (74 ° + 106 ° + 70 °)
    Thus d = 360° - (250 °)
    Thus d = 110 °

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