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    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° Correct Answer Incorrect Answer
    B 50° Correct Answer Incorrect Answer
    C 40° Correct Answer Incorrect Answer
    D 60° Correct Answer Incorrect Answer

    Solution

    Let the two interior angles on the same side of the transversal be x and y. Given, their difference is 20°.  x - y = 40° y = x -40°........(i) Since I and m are parallel and P is transversal Then, x + y = 180° ......[ Sum of interior angles is 180°] x + x -40° = 180° ...... [From equation (i)] 2x = 180° + 40° 2x = 220°   X =220°/2 = 110° Now, y = x -40° y = 110°-40° = 70° Smallest angles is 70° Therefore, the angles are 110° and 70°, respectively.

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