Mathematics
Grade9
Easy

Question

For what values of  is ABCD a parallelogram?

  1. 17 degree
  2. 21 degree
  3. 33 degree
  4. 9 degree

hintHint:

Polygon is a two- dimensional closed figure which is consist of three or more-line segments. Each polygon has different properties. One of the polygons is quadrilateral. Quadrilateral is a four-sided polygon with four angles and the sum of all angles of a quadrilateral is 360 degree . Here, we have to find the value of x in the given quadrilateral using the properties of the quadrilateral.

The correct answer is: 17 degree


    In the question there is a quadrilateral PQRS where angle Q equals 40 degree space a n d space angle S equals 3 x minus 11 degree.
    Here, we have to find the value of x for which the given quadrilateral is called as parallelogram.
    Since, the opposite angles of a parallelogram are equal.
    text  So,  end text
angle Q equals angle S
3 x minus 11 degree equals 40 degree
3 x equals 51 degree
x equals 17 degree
    So, the value of x for which the given quadrilateral is called as parallelogram is 17 degree.
    Therefore, the correct option is a, i.e., 17 degree.

    Parallelogram is a four-sided polygon whose opposite sides are parallel and equal to each other and the opposite angles are equal to each other. The sum of all angles of a parallelogram is 360 degree  and sum of two consecutive angles is 180 degree . The diagonals of a parallelogram bisect each other and the angle into two equal halves. Here, we have to use these properties of a parallelogram and solve the given question.

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