Question
Error Analysis Your friend incorrectly says that line m is parallel to line n when the measure of angle X is 73degrees. For which measure of angle X is line m parallel to line n? What was your friend's likely mistake?
107 degrees
Upper X
m
n
t
(The figure is not to scale.)
Question content area bottom
Part 1
Line m is parallel to line n when the measure of angle X is
enter your response heredegrees.
Part 2
What was your friend's likely mistake?
A.
Your friend found the complement of 107 degrees.
B.
Your friend found the supplement of 107 degrees.
C.
Your friend used the same measure for angle X as that of its alternate interior angle.
D.
Your friend used the same measure for angle X as that of its corresponding angle.
107 degrees
Upper X
m
n
t
(The figure is not to scale.)
Question content area bottom
Part 1
Line m is parallel to line n when the measure of angle X is
enter your response heredegrees.
Part 2
What was your friend's likely mistake?
A.
Your friend found the complement of 107 degrees.
B.
Your friend found the supplement of 107 degrees.
C.
Your friend used the same measure for angle X as that of its alternate interior angle.
D.
Your friend used the same measure for angle X as that of its corresponding angle.
Answers
GPT-4o mini
To determine the measure of angle X for which line m is parallel to line n, we first need to understand the relationships between angles formed when two lines are crossed by a transversal.
1. **Identifying Angle Relationships**: When two lines (m and n) are crossed by a transversal (t), several pairs of angles are formed:
- Corresponding angles
- Alternate interior angles
- Same-side interior angles
For lines m and n to be parallel, alternate interior angles or corresponding angles must be equal.
2. **Given Information**: Your friend says lines m and n are parallel when the measure of angle X is 73 degrees. This indicates that angle X corresponds to or is an alternate interior angle with an angle that measures 73 degrees.
If we assume angle X is the same as a corresponding angle or an alternate interior angle that measures 73 degrees, that means the angle on the other line (like angle Y) is also 73 degrees. For lines m and n to be parallel, angle X must be equal to the angle corresponding with it.
3. **Critical Calculation**:
If the correct angle for parallelism is 107 degrees, this means that angle X should also be 107 degrees for lines m and n to be parallel. Therefore, line m is parallel to line n when angle X measures:
**107 degrees.**
Part 2: **Your Friend's Mistake**:
- If your friend thought lines m and n were parallel at 73 degrees, they likely made a mistake regarding the angles involved. The most logical mistake would be:
**B. Your friend found the supplement of 107 degrees.**
This is because when one angle (like 73 degrees) is supplied (which is less than the required or true angle), then the supplement, which, when combined, gives you a straight line (180 degrees), is equal to 107 degrees.
Thus, the answers are:
- Angle X for parallelism: **107 degrees**.
- Likely mistake: **B. Your friend found the supplement of 107 degrees.**
1. **Identifying Angle Relationships**: When two lines (m and n) are crossed by a transversal (t), several pairs of angles are formed:
- Corresponding angles
- Alternate interior angles
- Same-side interior angles
For lines m and n to be parallel, alternate interior angles or corresponding angles must be equal.
2. **Given Information**: Your friend says lines m and n are parallel when the measure of angle X is 73 degrees. This indicates that angle X corresponds to or is an alternate interior angle with an angle that measures 73 degrees.
If we assume angle X is the same as a corresponding angle or an alternate interior angle that measures 73 degrees, that means the angle on the other line (like angle Y) is also 73 degrees. For lines m and n to be parallel, angle X must be equal to the angle corresponding with it.
3. **Critical Calculation**:
If the correct angle for parallelism is 107 degrees, this means that angle X should also be 107 degrees for lines m and n to be parallel. Therefore, line m is parallel to line n when angle X measures:
**107 degrees.**
Part 2: **Your Friend's Mistake**:
- If your friend thought lines m and n were parallel at 73 degrees, they likely made a mistake regarding the angles involved. The most logical mistake would be:
**B. Your friend found the supplement of 107 degrees.**
This is because when one angle (like 73 degrees) is supplied (which is less than the required or true angle), then the supplement, which, when combined, gives you a straight line (180 degrees), is equal to 107 degrees.
Thus, the answers are:
- Angle X for parallelism: **107 degrees**.
- Likely mistake: **B. Your friend found the supplement of 107 degrees.**