Question

important! angles must belong to the same transversal to be an angle pair. b. ∠7 and ∠14 alternate interior c. ∠3 and ∠6 none d. ∠9 and ∠16 none e. ∠4 and ∠7 f. ∠2 and ∠10 g. ∠8 and ∠14 h. ∠6 and ∠11 i. ∠4 and ∠13 j. ∠4 and ∠9

Explanation:

To solve for each angle pair, we analyze their positions relative to the transversals (lines \(a\), \(b\), and \(d\)):

Part e: \(\angle 4\) and \(\angle 7\)

• Step 1: Identify transversal. Both angles lie on the same transversal (the slanted line intersecting the horizontal and vertical lines).
• Step 2: Check position. \(\angle 4\) (interior, right) and \(\angle 7\) (interior, left) are on opposite sides of the transversal, between the two parallel lines (vertical and horizontal? Assume parallelism).
• Conclusion: Alternate Interior Angles.

Part f: \(\angle 2\) and \(\angle 10\)

• Step 1: Identify transversal. Both lie on transversal \(a\) (vertical line) and between the two horizontal lines (top and middle).
• Step 2: Check position. \(\angle 2\) (top, right of \(a\)) and \(\angle 10\) (middle, right of \(a\)) are in the same relative position (right of \(a\)) and on parallel lines (top horizontal and line \(d\)).
• Conclusion: Corresponding Angles.

Part g: \(\angle 8\) and \(\angle 14\)

• Step 1: Identify transversal. Both lie on transversal \(b\) (slanted line) and on the exterior of the two horizontal lines (top and middle).
• Step 2: Check position. \(\angle 8\) (top, right of \(b\)) and \(\angle 14\) (middle, right of \(b\)) are in the same relative position (right of \(b\)) and on parallel lines (top horizontal and line \(d\)).
• Conclusion: Corresponding Angles.

Part h: \(\angle 6\) and \(\angle 11\)

• Step 1: Check transversal. \(\angle 6\) lies on transversal \(b\) (slanted), \(\angle 11\) on transversal \(a\) (vertical). Different transversals.
• Conclusion: No angle pair (none).

Part i: \(\angle 4\) and \(\angle 13\)

• Step 1: Identify transversal. Both lie on the middle horizontal line \(d\) and between transversals \(a\) (vertical) and \(b\) (slanted).
• Step 2: Check position. \(\angle 4\) (left of \(b\), right of \(a\)) and \(\angle 13\) (left of \(b\), right of \(a\)) are consecutive interior angles (same - side interior) between \(a\) and \(b\).
• Conclusion: Consecutive Interior Angles.

Part j: \(\angle 4\) and \(\angle 9\)

• Step 1: Identify transversal. Both lie on transversal \(a\) (vertical) and on the interior of the two horizontal lines (top and middle).
• Step 2: Check position. \(\angle 4\) (top, right of \(a\)) and \(\angle 9\) (middle, left of \(a\)) are on opposite sides of \(a\), between the two horizontal lines.
• Conclusion: Alternate Interior Angles.

Final Answers (Filled Table):

Angle Pair	Relationship
f. \(\angle 2\) & \(\angle 10\)	Corresponding
g. \(\angle 8\) & \(\angle 14\)	Corresponding
h. \(\angle 6\) & \(\angle 11\)	None
i. \(\angle 4\) & \(\angle 13\)	Consecutive Interior
j. \(\angle 4\) & \(\angle 9\)	Alternate Interior

(Note: For each part, the key was analyzing transversal, parallel lines, and angle position (interior/exterior, same/opposite side).)

Answer:

To solve for each angle pair, we analyze their positions relative to the transversals (lines \(a\), \(b\), and \(d\)):

Part e: \(\angle 4\) and \(\angle 7\)

• Step 1: Identify transversal. Both angles lie on the same transversal (the slanted line intersecting the horizontal and vertical lines).
• Step 2: Check position. \(\angle 4\) (interior, right) and \(\angle 7\) (interior, left) are on opposite sides of the transversal, between the two parallel lines (vertical and horizontal? Assume parallelism).
• Conclusion: Alternate Interior Angles.

Part f: \(\angle 2\) and \(\angle 10\)

• Step 1: Identify transversal. Both lie on transversal \(a\) (vertical line) and between the two horizontal lines (top and middle).
• Step 2: Check position. \(\angle 2\) (top, right of \(a\)) and \(\angle 10\) (middle, right of \(a\)) are in the same relative position (right of \(a\)) and on parallel lines (top horizontal and line \(d\)).
• Conclusion: Corresponding Angles.

Part g: \(\angle 8\) and \(\angle 14\)

• Step 1: Identify transversal. Both lie on transversal \(b\) (slanted line) and on the exterior of the two horizontal lines (top and middle).
• Step 2: Check position. \(\angle 8\) (top, right of \(b\)) and \(\angle 14\) (middle, right of \(b\)) are in the same relative position (right of \(b\)) and on parallel lines (top horizontal and line \(d\)).
• Conclusion: Corresponding Angles.

Part h: \(\angle 6\) and \(\angle 11\)

• Step 1: Check transversal. \(\angle 6\) lies on transversal \(b\) (slanted), \(\angle 11\) on transversal \(a\) (vertical). Different transversals.
• Conclusion: No angle pair (none).

Part i: \(\angle 4\) and \(\angle 13\)

• Step 1: Identify transversal. Both lie on the middle horizontal line \(d\) and between transversals \(a\) (vertical) and \(b\) (slanted).
• Step 2: Check position. \(\angle 4\) (left of \(b\), right of \(a\)) and \(\angle 13\) (left of \(b\), right of \(a\)) are consecutive interior angles (same - side interior) between \(a\) and \(b\).
• Conclusion: Consecutive Interior Angles.

Part j: \(\angle 4\) and \(\angle 9\)

• Step 1: Identify transversal. Both lie on transversal \(a\) (vertical) and on the interior of the two horizontal lines (top and middle).
• Step 2: Check position. \(\angle 4\) (top, right of \(a\)) and \(\angle 9\) (middle, left of \(a\)) are on opposite sides of \(a\), between the two horizontal lines.
• Conclusion: Alternate Interior Angles.

Final Answers (Filled Table):

Angle Pair	Relationship
f. \(\angle 2\) & \(\angle 10\)	Corresponding
g. \(\angle 8\) & \(\angle 14\)	Corresponding
h. \(\angle 6\) & \(\angle 11\)	None
i. \(\angle 4\) & \(\angle 13\)	Consecutive Interior
j. \(\angle 4\) & \(\angle 9\)	Alternate Interior

(Note: For each part, the key was analyzing transversal, parallel lines, and angle position (interior/exterior, same/opposite side).)