Question

which set of equations is enough information to prove that lines a and b are parallel lines cut by transversal f?○ $mangle4 = 110^{circ}$ and $mangle3 = 70^{circ}$○ $mangle1 = 110^{circ}$ and $mangle2 = 110^{circ}$○ $mangle1 = 110^{circ}$ and $mangle3 = 70^{circ}$○ $mangle2 = 110^{circ}$ and $mangle3 = 110^{circ}$

Explanation:

Step1: Recall parallel line theorems

For two lines cut by a transversal, if consecutive interior angles are supplementary (sum to $180^\circ$), the lines are parallel.

Step2: Analyze Option A

Check if $\angle4$ and $\angle3$ are supplementary:
$m\angle4 + m\angle3 = 110^\circ + 70^\circ = 180^\circ$. These are consecutive interior angles, so lines $a$ and $b$ are parallel.

Step3: Verify other options

• Option B: $\angle1$ and $\angle2$ are vertical angles, their congruence does not relate to $a\parallel b$.
• Option C: $\angle1$ and $\angle3$ are corresponding angles; if they are not congruent ($110^\circ

eq70^\circ$), lines are not parallel.

• Option D: $\angle2$ and $\angle3$ are consecutive interior angles; their sum is $110^\circ+110^\circ=220^\circ

eq180^\circ$, so lines are not parallel.

Answer:

A. $m\angle4 = 110^\circ$ and $m\angle3 = 70^\circ$