Question

ing lines parallel
given: ( mparallel n ) and ( mangle2 + mangle3 = 180^{circ} )
prove: ( aparallel b )
fill in numbers to complete the proof.
enter your answers in the boxes,

Explanation:

Step1: Apply alternate interior angles theorem

Since \(m\parallel n\), by the alternate - interior angles theorem, \(\angle1\cong\angle2\).

Step2: Use substitution

We know that \(m\angle2 + m\angle3=180^{\circ}\). Substituting \(\angle1\) for \(\angle2\) (because \(\angle1\cong\angle2\)), we get \(m\angle1 + m\angle3 = 180^{\circ}\).

Answer:

1. \(\angle1\cong\angle2\) (so the number in the first box is \(2\))
2. \(m\angle1 + m\angle3=180^{\circ}\) (so the numbers in the second and third boxes are \(1\) and \(3\) respectively)