Question

each figure below is a parallelogram. use the properties you know to solve for the given variables. diagrams are not necessarily drawn to scale. 1) x = __ y = m∠m = m∠a = m∠i = __

Explanation:

Step1: Use opposite - angles property

In a parallelogram, opposite angles are equal. So, $\angle M=\angle P$.
$14x + 2=128$

Step2: Solve for $x$

Subtract 2 from both sides: $14x=128 - 2=126$. Then divide both sides by 14: $x=\frac{126}{14}=9$.

Step3: Use adjacent - angles property

Adjacent angles in a parallelogram are supplementary, i.e., $\angle P+\angle A = 180^{\circ}$. Also, $\angle I=\angle A$.
Since $\angle P = 128^{\circ}$, then $\angle A=180 - 128 = 52^{\circ}$.

Step4: Use opposite - angles property for $y$

$\angle A=\angle I$ and $\angle I = 5y+2$. Since $\angle A = 52^{\circ}$, we have $5y+2 = 52$. Subtract 2 from both sides: $5y=50$. Divide both sides by 5: $y = 10$.

Step5: Find angle measures

$m\angle M=128^{\circ}$ (from Step1), $m\angle A = 52^{\circ}$, $m\angle I=52^{\circ}$

Answer:

$x = 9$
$y = 10$
$m\angle M=128^{\circ}$
$m\angle A = 52^{\circ}$
$m\angle I=52^{\circ}$