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    If a transversal intersects two parallel lines, and the difference between two interior angles on the same side of the transversal is 40°, then find t
    Question

    If a transversal intersects two parallel lines, and the difference between two interior angles on the same side of the transversal is 40°, then find the smallest angle among the interior angles.

    A.

    70°

    B.

    50°

    C.

    40°

    D.

    60°

    Correct option is A

    Given:
    Two parallel lines are intersected by a transversal.
    The difference between two interior angles on the same side of the transversal is 40.40^\circ.​​
    Concept Used:
    When a transversal intersects two parallel lines, the sum of two interior angles on the same side of the transversal is 180180^\circ​ (since they are supplementary).
    Solution:
    According to the question;
    x + y = 180……..(i)
    x - y = 40 ………..(ii)
    Add the two equations:
    (x + y) + (x - y) = 180 + 40
    2x = 220
    x = 110
    Substituting x = 110 into the first equation:
    110 + y = 180
    y = 70
    The two angles are 110110^\circ​ and 70.70^\circ.​​
    Thus, The smallest angle among the interior angles is 70°.

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