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17 June, 06:56

If m□ebd=4x-8 and m□ebc=5x+20, find the value of x and m□ebc

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  1. 17 June, 07:13
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    m□ebd=4 x-8 and m□ebc=5 x+20

    This is solvable only if e b is the initial side and b d and b c lies on opposite side of each other and lies on a line i. e c, b, d are Collinear.

    ∠ebd and ∠ebc will form a linear pair. The meaning of linear pair is that angles forming on one side of a straight line through a common vertex which are adjacent is 180°.

    i. e

    ∠ ebd + ∠ebc = 180°

    4 x - 8 + 5x + 20 = 180°

    adding like terms

    ⇒ 9 x + 12 = 180°

    ⇒ 9 x = 180° - 12

    ⇒ 9 x = 168°

    ⇒ x = (168/9) ° = (56/3) °

    now m□ebc = 5 x + 20

    = 5 * 56/3 + 20

    = 280/3 + 20

    =340/3

    m□ebc = (340/3) °

    So, solution set is x = (56/3) ° and m□ebc = (340/3) °
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