Two parallel lines are cut by a transversal as shown below.Suppose =m∠6126°.  Find m∠1 and m∠4.

To find the measures of angles 1 and 4, we need to use the properties of parallel lines cut by a transversal.

1. Angle 1 and angle 6 are corresponding angles, as they are on the same side of the transversal and on the same side of the parallel lines. Therefore, m∠1 = m∠6.

2. Angle 6 and angle 2 are alternate interior angles, as they are on opposite sides of the transversal and between the parallel lines. Therefore, m∠6 = m∠2.

3. Angle 2 and angle 4 are corresponding angles, as they are on the same side of the transversal and on the same side of the parallel lines. Therefore, m∠2 = m∠4.

Since we know that m∠6 = 126°, we can conclude that m∠1 = m∠6 = 126°.

Similarly, since m∠2 = m∠4, we can conclude that m∠4 = m∠2 = 126°.

Therefore, m∠1 = 126° and m∠4 = 126°.