Question

name _ date _ unit 1 section 11 assignment - geometry 5. if ∠1 and ∠2 are a linear pair and ∠1 = 75°, what is the measure of ∠2? 6. true or false: if two lines are perpendicular to the same line, they are parallel to each other. explain

Explanation:

Step1: Recall linear - pair property

The sum of angles in a linear pair is 180°.
Let \(m\angle1 = 75^{\circ}\) and \(m\angle2\) be the other angle of the linear pair. So, \(m\angle1 + m\angle2=180^{\circ}\).

Step2: Solve for \(m\angle2\)

Substitute \(m\angle1 = 75^{\circ}\) into the equation \(m\angle1 + m\angle2 = 180^{\circ}\). Then \(m\angle2=180^{\circ}-m\angle1\).
\(m\angle2 = 180 - 75=105^{\circ}\)

For the second part:
In a plane, if two lines are perpendicular to the same line, they are parallel to each other. This is a well - known postulate in Euclidean geometry. So the statement "If two lines are perpendicular to the same line, they are parallel to each other" is True.

Answer:

1. \(m\angle2 = 105^{\circ}\)
2. True. In a plane, two lines perpendicular to the same line are parallel.