Question

given rhombus efgh below. if $m\angle hie = (-2x + 6)^\circ$, solve for $x$.

Explanation:

Step1: Recall rhombus diagonal property

The diagonals of a rhombus are perpendicular, so $m\angle HIE = 90^\circ$.

Step2: Set up equation for $x$

$$-2x + 6 = 90$$

Step3: Isolate the $x$-term

Subtract 6 from both sides:
$$-2x = 90 - 6$$
$$-2x = 84$$

Step4: Solve for $x$

Divide by -2:
$$x = \frac{84}{-2}$$

Answer:

$x = -42$