Question

10 in the figure shown two parallel lines are being cut by a transversal. label the angle relationships as alternate interior, corresponding, vertical, or supplementary.
a. ∠1 and ∠2
b. ∠4 and ∠6
c. ∠7 and ∠5
d. ∠2 and ∠6
e. ∠4 and ∠5
f. ∠3 and ∠5

Explanation:

Step1: Recall angle - relationship definitions

• Alternate interior angles: Two non - adjacent interior angles on opposite sides of the transversal.
• Corresponding angles: Angles in the same relative position.
• Vertical angles: Opposite angles formed by two intersecting lines.
• Supplementary angles: Two angles whose sum is \(180^{\circ}\).

Step2: Analyze each pair

• For \(∠4\) and \(∠6\):

They are non - adjacent interior angles on opposite sides of the transversal. So, \(∠4\) and \(∠6\) are alternate interior angles.

• For \(∠7\) and \(∠5\):

They are in the same relative position. So, \(∠7\) and \(∠5\) are corresponding angles.

• For \(∠2\) and \(∠6\):

They are in the same relative position. So, \(∠2\) and \(∠6\) are corresponding angles.

• For \(∠4\) and \(∠5\):

They are adjacent and form a linear pair (\(∠4 + ∠5=180^{\circ}\)). So, \(∠4\) and \(∠5\) are supplementary angles.

• For \(∠3\) and \(∠5\):

They are opposite angles formed by two intersecting lines. So, \(∠3\) and \(∠5\) are vertical angles.

Answer:

a. \(∠1\) and \(∠2\): supplementary
b. \(∠4\) and \(∠6\): alternate interior
c. \(∠7\) and \(∠5\): corresponding
d. \(∠2\) and \(∠6\): corresponding
e. \(∠4\) and \(∠5\): supplementary
f. \(∠3\) and \(∠5\): vertical