Question

Find the x step by step

Answer 1

Angles are equal as it's parallelogram

• 6x²-15=5x²-2x
• x²-15=-2x
• x²+2x-15=0
• x²-3x+5x-15=0
• x(x-3)+5(x-3)=0
• (x+5)(x-3)=0
• x=-5 and 3

Answer 2

x = 3

Explanation:

Assuming the given shape is a rhombus.

Properties of a rhombus

• Quadrilateral (4-sided shape)
• All 4 sides are equal in length
• Opposite angles are equal
• Reflection of symmetry over both diagonals

As there is a reflection of symmetry over the diagonals, the diagonals bisect the vertices, i.e. the diagonal divides the vertices into 2 equal angles. Therefore, the angles either side of the diagonal at each vertex are equal.

Therefore:

`\implies 6x^2-15=5x^2-2x`

Rearrange to create a quadratic (equal to zero):

`\implies 6x^2-15-5x^2+2x=0`

`\implies x^2+2x-15=0`

Solve the quadratic to find the value of x:

`\implies x^2+2x-15=0`

`\implies x^2+5x-3x-15=0`

`\implies x(x+5)-3(x+5)=0`

`\implies (x-3)(x+5)=0`

Therefore:

`(x-3)=0 \implies x=3`

`(x+5)=0 \implies x=-5`

Substitute the found values of x into one of the expressions:

`x=3 \implies 6(3)^2-15=39`

`x=-5 \implies 6(-5)^2-15=135`

Therefore, the options for the angles are 39° or 135°.

From inspection of the diagram, the angles are clearly acute (less than 90°), therefore the only appropriate value of x is 3.