Mathematics
Grade9
Easy

Question

The measure of angle x is ____________.

  1. 65 degree
  2. 55 degree
  3. 60 degree
  4. 50 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 measure of angle x in the given quadrilateral using the properties of the quadrilateral.

The correct answer is: 65 degree


    In the question there are two parallelograms ABCD and CDEF as shown in the figure above.
    Here, we have to find the measure of angle x.
    Since, the consecutive angles of a parallelogram are supplementary.
    So,
    text  In parallelogram  end text ABCD comma
angle A D C equals angle B C D
rightwards double arrow 60 degree plus angle x plus 55 degree equals 180 degree
rightwards double arrow angle x equals 65 degree
    Thus, the measure of angle x is 65 degree.
    Therefore, the correct option is a, i.e., 65 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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