Question

1. l || m

m∠1 =
m∠2 =
m∠3 =
m∠4 =
m∠5 =

Explanation:

Step1: Use corresponding - angles property

Since \(l\parallel m\), \(\angle1\) and the \(73^{\circ}\) angle are corresponding - angles. So \(m\angle1 = 73^{\circ}\).

Step2: Use angle - sum property of a triangle

In the triangle, the sum of interior angles is \(180^{\circ}\). Let the third - angle in the triangle be \(x\). We know one angle is \(49^{\circ}\) and we just found \(\angle1 = 73^{\circ}\). Then \(m\angle2=180^{\circ}-(73^{\circ}+49^{\circ}) = 58^{\circ}\).

Step3: Use vertical - angles property

\(\angle3\) and the \(73^{\circ}\) angle are vertical angles. So \(m\angle3 = 73^{\circ}\).

Step4: Use alternate - interior angles property

Since \(l\parallel m\), \(\angle4\) and \(\angle2\) are alternate - interior angles. So \(m\angle4 = 58^{\circ}\).

Step5: Use corresponding - angles property

\(\angle5\) and \(\angle4\) are corresponding angles. So \(m\angle5 = 58^{\circ}\).

Answer:

\(m\angle1 = 73^{\circ}\), \(m\angle2 = 58^{\circ}\), \(m\angle3 = 73^{\circ}\), \(m\angle4 = 58^{\circ}\), \(m\angle5 = 58^{\circ}\)