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