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7 July, 19:31

If x = 10, which lines are parallel? Check all that apply.

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  1. 7 July, 19:40
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    b||c; c||d; b||d

    Step-by-step explanation:

    Substituting 10 for x, in the angle beside b we have

    7 (10) - 5 = 70-5 = 65

    In the angle beside c we have

    10 (10) + 15 = 100+15 = 115

    In the angle beside d we have

    12 (10) - 5 = 120-5 = 115

    In the angle beside we have

    8 (10) - 25 = 80-25 = 55

    The angle beside c has a vertical angle on the other side of c. This angle would be same-side interior angles with the angle beside b; this is because they are inside the block of lines made by b and c and on the same side of a, the transversal. These two angles are supplementary; this is because 65+115 = 180. Since these angles are supplementary, this means that b||c.

    The angle beside c and the angle beside d would be alternate interior angles; this is because they are inside the block of lines made by c and d and on opposite sides of the transversal. These two angles are congruent; this means that c||d.

    Since b||c and c||d, by the transitive property, b||d.
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