Question

in order for the parallelogram to be a rhombus, x=?

Answer 1

$\\ \large\sf\longmapsto x + 15 = 2x - 40 \\ \\ \large\sf\longmapsto x - 2x = - 40 - 15 \\ \\ \large\sf\longmapsto - x = - 55\\ \large\sf\longmapsto x = 55$

Answer 2

The value of x is 55 degrees.

What is rhombus?

A rhombus is a diamond-shaped quadrilateral that has all four sides equal

What are the properties of a rhombus?

The properties of a rhombus are:

1. Opposite angles are equal.
2. All sides are equal and, opposite sides are parallel to each other.
3. Diagonals bisect each other perpendicularly.
4. Sum of any two adjacent angles is 180°

According to the given question.

We have a rhombus.

Since, we know that the diagonals of the rhombus bisect the angles.

Therefore,

$(x+15)^{o} = (2x-40)^{o}$

Solve, the above expression for x.

$\implies x +15 = 2x -40\\\implies 15+40 = 2x -x \\\implies 55 = x \\0r\ x = 55^{o}$

Hence, the value of x is 55 degrees.

Find out more information about rhombus here:

https://brainly.com/question/12189679

#SPJ2