2 Answers

Dwbartz · Answer 1 · 2020-01-30T10:23:03+0000

Answer:

C. 28

Explanation:

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

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.

$\implies (6x)/(6)=(168)/(6)$

$\therefore x=28$

The correct answer is C.

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