Given ABC=65 and BCD=105. Is it possible that Line AB intersects line CD​

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Given ABC=65 and BCD=105. Is it possible that Line AB intersects line CD​

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Khải Quang 4 years 2021-07-28T21:53:57+00:00 1 Answers 15 views 0

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  1. trungdung22
    0
    2021-07-28T21:55:25+00:00
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    Given:

    m\angle ABC=65^\circ

    m\angle BCD=105^\circ

    To find:

    Whether it is possible that Line AB intersects line CD​.

    Solution:

    We have,

    m\angle ABC=65^\circ

    m\angle BCD=105^\circ

    The angles m\angle ABC and m\angle BCD are same sided interior angles.

    If two lines are parallel and a transversal line intersect them, then the same sided interior angles are supplementary angles and their sum is 180 degrees.

    m\angle ABC+m\angle BCD=65^\circ+105^\circ

    m\angle ABC+m\angle BCD=170^\circ

    m\angle ABC+m\angle BCD\neq 180^\circ

    So, the lines AB and CD are not parallel to each other.

    Therefore, the intersection of lines AB and CD is possible.

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