Question
In each diagram, line k is parallel to line l, and line t intersects lines k and l.
Based on the diagram, which statement is true?
Responses
A The value of x is 70, because the two angles shown in each diagram are congruent. The value of x is 70, because the two angles shown in each diagram are congruent.
B The value of x is 110, because the two angles shown in each diagram are supplementary. The value of x is 110, because the two angles shown in each diagram are supplementary.
C The value of x is 70, because the two angles shown in each diagram are complementary. The value of x is 70, because the two angles shown in each diagram are complementary.
D The value of x is 110, because the two angles shown in each diagram are congruent.
Based on the diagram, which statement is true?
Responses
A The value of x is 70, because the two angles shown in each diagram are congruent. The value of x is 70, because the two angles shown in each diagram are congruent.
B The value of x is 110, because the two angles shown in each diagram are supplementary. The value of x is 110, because the two angles shown in each diagram are supplementary.
C The value of x is 70, because the two angles shown in each diagram are complementary. The value of x is 70, because the two angles shown in each diagram are complementary.
D The value of x is 110, because the two angles shown in each diagram are congruent.
Answers
GPT-4o mini
To determine which statement is true regarding the value of x when line k is parallel to line l and line t intersects these lines, we need to consider the relationships between the angles formed.
1. **Congruent Angles:** When two lines are crossed by another line (the transversal), the pairs of angles that are formed can be congruent under certain conditions:
- Corresponding angles: Angles that are in the same relative position at each intersection.
- Alternate interior angles: Angles that lie between the two lines and on opposite sides of the transversal.
2. **Supplementary Angles:** The angles formed can also be supplementary (adding up to 180 degrees) under situations such as:
- Same-side interior angles: Located on the same side of the transversal and inside the two lines.
3. **Complementary Angles:** The angles that sum to 90 degrees fall under the category of complementary angles, typically not applicable here since we are dealing with parallel lines and a transversal.
**Evaluating the Provided Options:**
- **A (Congruent angles):** If the angles shown are congruent, then x could indeed be 70 if both angles measure 70 degrees each.
- **B (Supplementary angles):** If the angles shown are supplementary, x could be found as 110 if they sum to 180 degrees (70 + 110 = 180).
- **C (Complementary angles):** This option would be incorrect, as the angles in the context given cannot be complementary with parallel lines and a transversal.
- **D (Congruent angles):** If the two angles are congruent and their measure is indicated as x equaling 110, that’s possible depending on the specific angles in question.
Based on typical angle relationships when two parallel lines are intersected by a transversal:
- If x = 70, it would mean the relevant angles are congruent (as in option A).
- If x = 110, it would mean the relevant angles are supplementary (as in option B).
Without a clear diagram, the reasoning aligns primarily with Congruence (option A) or Supplementarity (option B). **Assuming that we regard the standard parallel line intersections, the most likely outcome is that option A holds true: "The value of x is 70, because the two angles shown in each diagram are congruent."** However, option B could also be valid if the angles are supplementary.
Thus, assuming angles are indicated as 70 and 110 as described, the most plausible and straightforward correct answer (given common angle relationships involving parallel lines) is:
**A. The value of x is 70, because the two angles shown in each diagram are congruent.**
1. **Congruent Angles:** When two lines are crossed by another line (the transversal), the pairs of angles that are formed can be congruent under certain conditions:
- Corresponding angles: Angles that are in the same relative position at each intersection.
- Alternate interior angles: Angles that lie between the two lines and on opposite sides of the transversal.
2. **Supplementary Angles:** The angles formed can also be supplementary (adding up to 180 degrees) under situations such as:
- Same-side interior angles: Located on the same side of the transversal and inside the two lines.
3. **Complementary Angles:** The angles that sum to 90 degrees fall under the category of complementary angles, typically not applicable here since we are dealing with parallel lines and a transversal.
**Evaluating the Provided Options:**
- **A (Congruent angles):** If the angles shown are congruent, then x could indeed be 70 if both angles measure 70 degrees each.
- **B (Supplementary angles):** If the angles shown are supplementary, x could be found as 110 if they sum to 180 degrees (70 + 110 = 180).
- **C (Complementary angles):** This option would be incorrect, as the angles in the context given cannot be complementary with parallel lines and a transversal.
- **D (Congruent angles):** If the two angles are congruent and their measure is indicated as x equaling 110, that’s possible depending on the specific angles in question.
Based on typical angle relationships when two parallel lines are intersected by a transversal:
- If x = 70, it would mean the relevant angles are congruent (as in option A).
- If x = 110, it would mean the relevant angles are supplementary (as in option B).
Without a clear diagram, the reasoning aligns primarily with Congruence (option A) or Supplementarity (option B). **Assuming that we regard the standard parallel line intersections, the most likely outcome is that option A holds true: "The value of x is 70, because the two angles shown in each diagram are congruent."** However, option B could also be valid if the angles are supplementary.
Thus, assuming angles are indicated as 70 and 110 as described, the most plausible and straightforward correct answer (given common angle relationships involving parallel lines) is:
**A. The value of x is 70, because the two angles shown in each diagram are congruent.**