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4 February, 07:59

Use a definition, postulate, or theorem to find the value of x in the figure described.


< means angle

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  1. 4 February, 08:24
    0
    The value of x is 47

    Step-by-step explanation:

    * Lets explain the meaning of linear pair of angles

    - A linear pair of angles is formed when two lines intersect

    - If two angles are adjacent angles formed by two intersecting lines,

    then the two angles are a linear pair of angles

    - The measure of a straight angle is 180°, then the measure of the

    linear pair of angles is 180°

    - That means the sum of the measures of the two angles is 180°

    * Lets solve the problem

    ∵ ∠ABC and ∠CBD are a linear pair angles

    ∴ m∠ABC + m∠CBD = 180°

    - The measures of the two angles are equal

    ∵ m∠ABC = m∠CBD = (2x - 4) °

    - To find the value of x equate the sum of them by 180

    ∴ (2x - 4) + (2x - 4) = 180

    - Collect like terms in the left hand side

    ∵ (2x + 2x) + (-4 + - 4) = 180

    ∴ 4x + - 8 = 180

    - Remember (+) (-) = (-)

    ∴ 4x - 8 = 180

    - Add 8 to both sides

    ∴ 4x = 188

    - Divide both sides by 4

    ∴ x = 47

    ∴ The value of x is 47
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