Question
Examine the diagram.
Lines b and a intersect lines c and d to form 16 angles. At the intersection of lines b and c, clockwise from top left, the angles are 1, 2, 4, 3. At a and c, clockwise from top left, the angles are 5, 6, 8, 7. At b and d, clockwise from top left, the angles are 13, 14, 16, 15. At a and d, clockwise from top left, the angles are 9, 10, 12, 11.
Name two corresponding angles to ∠1.
∠6 and ∠15
∠5 and ∠6
∠13 and ∠15
∠5 and ∠13
Lines b and a intersect lines c and d to form 16 angles. At the intersection of lines b and c, clockwise from top left, the angles are 1, 2, 4, 3. At a and c, clockwise from top left, the angles are 5, 6, 8, 7. At b and d, clockwise from top left, the angles are 13, 14, 16, 15. At a and d, clockwise from top left, the angles are 9, 10, 12, 11.
Name two corresponding angles to ∠1.
∠6 and ∠15
∠5 and ∠6
∠13 and ∠15
∠5 and ∠13
Answers
GPT-4o mini
To determine the corresponding angles to ∠1, we must first clarify the definition of corresponding angles. Corresponding angles are formed when a transversal intersects two parallel lines, and they are located in the same relative position at each intersection.
In the given diagram:
- Lines c and d are intersected by lines a and b.
- The angles are defined as follows:
- At the intersection of lines b and c: angles are labeled ∠1, ∠2, ∠3, ∠4.
- At the intersection of lines a and c: angles are labeled ∠5, ∠6, ∠7, ∠8.
- At the intersection of lines b and d: angles are labeled ∠13, ∠14, ∠15, ∠16.
- At the intersection of lines a and d: angles are labeled ∠9, ∠10, ∠11, ∠12.
Since ∠1 is located at the intersection of b and c, we will look for angles at the intersections of lines a and c (which would correspond with ∠1) and lines b and d (which would also correspond with ∠1).
When comparing their positions:
- At the intersection of lines a and c (where ∠5, ∠6, ∠7, ∠8 are), the corresponding angle to ∠1 is ∠5.
- At the intersection of lines b and d (where ∠13, ∠14, ∠15, ∠16 are), the corresponding angle to ∠1 is ∠13.
Thus, the two corresponding angles to ∠1 are ∠5 (from a and c) and ∠13 (from b and d).
Therefore, the correct group of corresponding angles to ∠1 is:
**∠5 and ∠13.**
In the given diagram:
- Lines c and d are intersected by lines a and b.
- The angles are defined as follows:
- At the intersection of lines b and c: angles are labeled ∠1, ∠2, ∠3, ∠4.
- At the intersection of lines a and c: angles are labeled ∠5, ∠6, ∠7, ∠8.
- At the intersection of lines b and d: angles are labeled ∠13, ∠14, ∠15, ∠16.
- At the intersection of lines a and d: angles are labeled ∠9, ∠10, ∠11, ∠12.
Since ∠1 is located at the intersection of b and c, we will look for angles at the intersections of lines a and c (which would correspond with ∠1) and lines b and d (which would also correspond with ∠1).
When comparing their positions:
- At the intersection of lines a and c (where ∠5, ∠6, ∠7, ∠8 are), the corresponding angle to ∠1 is ∠5.
- At the intersection of lines b and d (where ∠13, ∠14, ∠15, ∠16 are), the corresponding angle to ∠1 is ∠13.
Thus, the two corresponding angles to ∠1 are ∠5 (from a and c) and ∠13 (from b and d).
Therefore, the correct group of corresponding angles to ∠1 is:
**∠5 and ∠13.**