Question

Figure ABCD is a parallelogram. If ABCD is also a rhombus, what must be the value of x? 13 15 18 23

Answer 1

Answer:

x = 13

Step-by-step explanation:

To solve for x in a parallelogram ABCD, which is also a rhombus, one must recall the common properties of parallelogram and rhombus.

One of the properties say that diagonals are perpendicular bisectors of each other, It means that the triangles formed in the figure are right-angles triangle.

Therefore, to calculate the value of x we can write:

(5x - 35) = 90 because it is the right angled triangle.

5x = 90 - 35

5x = 65

x = 65/5

x = 13

Answer 2

Answer: First option 13

Solution

If ABCD is a rhombus, the diagonals must be perpendicular, then the angle (5x+25)° must be a right angle (90°):

(5x+25)°=90°

5x+25=90

Solving for x: Subtracting 25 both sides of the equation:

5x+25-25=90-25

Subtracting:

5x=65

Dividing both sides of the equation by 5:

5x/5=65/5

Dividing:

x=13

Answer: The value of x must be 13