Question

what is the value of x

Answer 1

Answer:

Correct me if I am wrong, but I believe it is B.

Step-by-step explanation:

Answer 2

Answer:

C. 28

Step-by-step explanation:

From the diagram diagram; $\angle BAC=(x+6)\degree$ and $\angle ABD=2x\degree$.

• The opposite sides of a rhombus are parallel.
• The diagonals act as transversals.
• Therefore the co-interior angles will add up to 180 degrees.

The pair of co-interior angles are $\angle BAD$ and $\angle ABC$.

Also the diagonals of a rhombus bisect corner angles.

This implies that:

$\angle BAD=2(\angle BAC)\implies \angle BAD=2(x+6)\degree$.

$\angle ABC=2(\angle ABD)\implies \angle ABC=2(2x)\degree$.

The co-interior angles are supplementary  so we form the equation:

$\angle BAD+\angle ABC=180\degree$

$\implies 2(x+6)\degree+2(2x)\degree=180\degree$

Expand the parenthesis to get:

$\implies 2x+12+4x=180\degree$

Group the similar terms:

$\implies 2x+4x=180-12$

Simplify

$\implies 6x=168$

Divide both sides by 6.

$\implies \frac{6x}{6}=\frac{168}{6}$

$\therefore x=28$

The correct answer is C.