Question

1. find the value of each variable in the parallelogram. round your answers to the nearest tenth, if necessary.

in parallelogram hjkl, the measure of angle h is $(3x - 2)^{circ}$, the measure of angle l is $(2x + 2)^{circ}$, the measure of angle j is $(2y + 22)^{circ}$

Explanation:

Step1: Use consecutive angles property

In a parallelogram, consecutive angles are supplementary (sum to $180^\circ$). For angles $\angle H$ and $\angle L$:
$$(3x - 2) + (2x + 2) = 180$$

Step2: Simplify and solve for $x$

Combine like terms and isolate $x$:
$$5x = 180$$
$$x = \frac{180}{5} = 36$$

Step3: Use opposite angles property

In a parallelogram, opposite angles are equal. $\angle J = \angle L$, so:
$$2y + 22 = 2x + 2$$

Step4: Substitute $x=36$ and solve for $y$

Plug in $x$ value and isolate $y$:
$$2y + 22 = 2(36) + 2$$
$$2y + 22 = 74$$
$$2y = 74 - 22 = 52$$
$$y = \frac{52}{2} = 26$$

Answer:

$x = 36$, $y = 26$