Mathematics
Grade9
Easy

Question

If STUV is a parallelogram, then the value of x must be ___________.

  1. 39 degree
  2. 35 degree
  3. 45 degree
  4. 60 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: 35 degree


    In the question there is a parallelogram STUV as shown in the figure above.
    Here, we have to find the value of x in the above figure.
    Since, the consecutive angles of a parallelogram are supplementary.
    text  So,  end text
angle T plus angle U equals 180 degree
rightwards double arrow angle T equals 180 degree minus angle U
rightwards double arrow angle T equals 180 degree minus 70 degree
rightwards double arrow 3 x plus 5 degree equals 110 degree
rightwards double arrow 3 x equals 105 degree
rightwards double arrow x equals 35 degree
    Thus, the value of x is 35 degree.
    Therefore, the correct option is b, i.e., 35 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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