Question

the interior angle of point b measures(3x - 7) degrees and the interior angle of point d measures (x + 15) degrees. what is the value of x? (1 point) o 11 o 25 o 43 o 22

Explanation:

Step1: Recall the property of a parallelogram

In a parallelogram, opposite angles are equal and consecutive angles are supplementary. Here, \( \angle B=(3x - 7)^{\circ}\) and \( \angle D=(x + 15)^{\circ}\). Since \( \angle B\) and \( \angle D\) are consecutive angles in a parallelogram, \( \angle B+\angle D = 180^{\circ}\) (consecutive angles of a parallelogram are supplementary).

Step2: Set up the equation

Substitute the expressions for \( \angle B\) and \( \angle D\) into the supplementary - angle equation:

$$
LATEXBLOCK0
$$

Step3: Solve the equation for \(x\)

Subtract 8 from both sides of the equation:

$$
LATEXBLOCK1
$$

Divide both sides by 4:

$$ x=\frac{172}{4}=43 $$

Answer:

\(43\)