Mathematics
Easy

Question

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

Hint:

## 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 = 18010k = 180-90+1010k = 90+1010k = 100k = 100/10k =10So, 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.