Mathematics
Grade9
Easy

Question

If WXYZ is a rectangle, then the value of k is _______.

  1. 7
  2. 12
  3. 5
  4. 10

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. Here, we have to find the value of k in the given quadrilateral using the properties of the quadrilateral.

The correct answer is: 10


    In the question there is a diagram of a rectangle called WXYZ using which we have to find the value of k.
    Since, WXYZ is a rectangle so, all the angles of a rectangle measure 90°.
    So, Angle XYZ is 90°.
    As shown in the diagram, diagonal XZ divides the rectangle in two triangles.
    Triangle XYZ has three angles, angle XYZ, angle XZY, angle YXZ which measures 90°, 3k-10° and 7k respectively.
    We, know that the sum of measurements of three angles of a triangle is always 180°.
    So, we can say that,
    7k+3k-10+90 = 180
    rightwards double arrow10k = 180-90+10
    rightwards double arrow10k = 90+10
    rightwards double arrow10k = 100
    rightwards double arrowk = 100/10
    rightwards double arrowk =10
    So, the value of k is 10.
    Therefore, the correct option is d, i.e., 10.

    Rectangle is a four- sided polygon whose opposite sides are equal and parallel to each other. In rectangle each angle is 90 degree and sum of all angles is 360 degree . The diagonals are equal in measure and they bisect each other. Here, we have to use the properties of rectangle in order to solve the above question.

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