Question

4520va v geometry sem a geometry proving lines parallel which set of equations is enough information to prove that lines a and b are parallel lines cut by transversal f? ( mangle2 = 110^{circ} ) and ( mangle3 = 110^{circ} ) ( mangle4 = 110^{circ} ) and ( mangle3 = 70^{circ} ) ( mangle1 = 110^{circ} ) and ( mangle2 = 110^{circ} ) ( mangle1 = 110^{circ} ) and ( mangle3 = 70^{circ} )

Explanation:

Step1: Recall the property of parallel lines

If two lines are parallel and cut by a transversal, then corresponding angles are equal.

Step2: Analyze each option

• For \(m\angle2 = 110^{\circ}\) and \(m\angle3 = 110^{\circ}\): \(\angle2\) and \(\angle3\) are not corresponding angles.
• For \(m\angle4 = 110^{\circ}\) and \(m\angle3 = 70^{\circ}\): These angles do not satisfy the condition for parallel lines.
• For \(m\angle1 = 110^{\circ}\) and \(m\angle2 = 110^{\circ}\): \(\angle1\) and \(\angle2\) are corresponding angles. If corresponding angles are equal, then the lines \(a\) and \(b\) are parallel.
• For \(m\angle1 = 110^{\circ}\) and \(m\angle3 = 70^{\circ}\): These angles do not satisfy the condition for parallel lines.

Answer:

\(m\angle1 = 110^{\circ}\) and \(m\angle2 = 110^{\circ}\)