Question
If WXYZ is a rectangle, then the value of k is _______.
- 7
- 12
- 5
- 10
Hint:
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
10k = 180-90+10
10k = 90+10
10k = 100
k = 100/10
k =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 
and sum of all angles is 
. 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.
Related Questions to study
If STUV is a parallelogram, the value of 
must be ___________.
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 and sum of two consecutive angles is 
. 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.
If STUV is a parallelogram, the value of must be ___________.
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 and sum of two consecutive angles is . 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.
If the length of the suitcase is 12 cm and breadth is 6 cm, what is the perimeter of the suitcase?
Rectangle is a four- sided polygon whose opposite sides are equal and parallel to each other. In rectangle each angle is and sum of all angles is . 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.
If the length of the suitcase is 12 cm and breadth is 6 cm, what is the perimeter of the suitcase?
Rectangle is a four- sided polygon whose opposite sides are equal and parallel to each other. In rectangle each angle is and sum of all angles is . 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.
The perimeter of LONMP is _______.
The perimeter of LONMP is _______.
If 
, then the measure of 
= _____________.
If , then the measure of = _____________.
In the envelope ACDB, if AD = 7 cm, then find the length of diagonal BC.
In the envelope ACDB, if AD = 7 cm, then find the length of diagonal BC.
The value of g in parallelogram PQRS is ____.
Opposite sides are parallel ( distance between the opposite sides will be equal)
Opposite sides are congruent.
Opposite angles are same and congruent as well.
diagonals of a parallelogram bisect each other.
Each diagonal of a parallelogram separates it into two congruent triangles.
Same-Side interior angles (consecutive angles) are supplementary
The value of g in parallelogram PQRS is ____.
Opposite sides are parallel ( distance between the opposite sides will be equal)
Opposite sides are congruent.
Opposite angles are same and congruent as well.
diagonals of a parallelogram bisect each other.
Each diagonal of a parallelogram separates it into two congruent triangles.
Same-Side interior angles (consecutive angles) are supplementary
if STAY is a rectangle.
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