not equal.
8. Suppose $\mathrm{m} \angle 3=(4 x+12)^{\circ}$ and $\mathrm{m} \angle 7=(80-x)^{\circ}$, where $x=15$. Are the lines parallel? Explain.
Answer
Final Answer: The lines are \(\boxed{\text{not parallel}}\) because the measures of the corresponding angles are not equal. Specifically, \(\angle 3 = 72^\circ\) and \(\angle 7 = 65^\circ\).
Step 1 ：We are given that the measure of angle 3 is \((4x+12)^\circ\) and the measure of angle 7 is \((80-x)^\circ\), where \(x=15\).
Step 2 ：We need to determine if the lines are parallel. The lines will be parallel if the corresponding angles are equal.
Step 3 ：Substitute the given value of \(x\) into the expressions for the measures of these angles.
Step 4 ：Substituting \(x=15\) into the expression for the measure of angle 3, we get \(\angle 3 = 72^\circ\).
Step 5 ：Substituting \(x=15\) into the expression for the measure of angle 7, we get \(\angle 7 = 65^\circ\).
Step 6 ：Since the measures of the corresponding angles are not equal, the lines are not parallel.
Step 7 ：Final Answer: The lines are \(\boxed{\text{not parallel}}\) because the measures of the corresponding angles are not equal. Specifically, \(\angle 3 = 72^\circ\) and \(\angle 7 = 65^\circ\).
