Question

Find the value of x that makes the quadrilateral a parallelogram?

Answer 1

5

Explanation:

since the sides of parallelogram are parallel

then 3X+3 = 4X-2 (they are equal because they are alternating angles )

3X+3 = 4X-2 subtract 3X from both sides

3 = X-2. add 2 to both sides

X= 5

Answer 2

x = 5

Explanation:

As the diagonals of a parallelogram bisect each other (divide into two equal parts):

`\implies 2x+1=x+6`

`\implies 4x-2=3x+3`

Solve the first equation for x:

`\implies 2x+1-1=x+6-1`

`\implies 2x=x+5`

`\implies 2x-x=x+5-x`

`\implies x=5`

Solve the second equation for x:

`\implies 4x-2+2=3x+3+2`

`\implies 4x=3x+5`

`\implies 4x-3x=3x+5-3x`

`\implies x=5`

Therefore, the value of x that makes the quadrilateral a parallelogram is:

• x = 5