Question

jklm is a parallelogram. what is m∠j? (9y + 1)° (y + 17)° (not drawn to scale) a 2 b 19 c 161 d 29

Explanation:

Step1: Use property of parallelogram

In a parallelogram, adjacent - angles are supplementary. So, $\angle J+\angle L = 180^{\circ}$. Given $\angle J=(9y + 1)^{\circ}$ and $\angle L=(y + 17)^{\circ}$, we have the equation $(9y + 1)+(y + 17)=180$.

Step2: Simplify the equation

Combine like - terms: $9y+y+1 + 17=180$, which simplifies to $10y+18 = 180$.

Step3: Solve for y

Subtract 18 from both sides: $10y=180 - 18=162$. Then divide both sides by 10: $y=\frac{162}{10}=16.2$.

Step4: Find the measure of $\angle J$

Substitute $y = 16.2$ into the expression for $\angle J$: $\angle J=(9y + 1)^{\circ}=(9\times16.2+1)^{\circ}=(145.8 + 1)^{\circ}=146.8^{\circ}$. But there is a mistake above. The correct property to use is that opposite angles in a parallelogram are equal. So $\angle J=\angle L$.

Step5: Correctly set up the equation

Set $9y + 1=y + 17$.

Step6: Solve the correct equation

Subtract y from both sides: $9y - y+1=y - y + 17$, which gives $8y+1 = 17$. Subtract 1 from both sides: $8y=17 - 1 = 16$. Divide both sides by 8: $y = 2$.

Step7: Calculate $\angle J$

Substitute $y = 2$ into the expression for $\angle J$: $\angle J=(9y + 1)^{\circ}=(9\times2+1)^{\circ}=(18 + 1)^{\circ}=19^{\circ}$.

Answer:

B. 19