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

finding the value of x in the rhombus ABCD made by the diagonals

Solution:

Given, ABCD is a parallelogram.

Some of the important properties of the rhombus are:

  • All sides of the rhombus are equal.
  • The opposite sides of a rhombus are parallel.
  • Opposite angles of a rhombus are equal.
  • In a rhombus, diagonals bisect each other at right angles.
  • Diagonals bisect the angles of a rhombus.

If ABCD is a rhombus, the diagonals must be perpendicular.

So, the angle (5x + 25)° must be a right angle (90°).

5x + 25 = 90

5x = 90 - 25

5x = 65

x = 65/5

x = 13

Therefore, the value of x is 13°.

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

Summary:

Figure ABCD is a parallelogram. If ABCD is also a rhombus, the value of x is 13°.

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