Question

given rhombus efgh below. if m∠hie = (-2x + 6)°, solve for x.

Explanation:

Step1: Recall rhombus diagonal property

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

Step2: Set up equation for $x$

Equate the given angle expression to 90:
$$-2x + 6 = 90$$

Step3: Isolate the variable term

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

Step4: Solve for $x$

Divide both sides by $-2$:
$$x = \frac{84}{-2}$$
$$x = -42$$

Answer:

$x = -42$