Which lines are parallel if m1 + m2 = 180? Justify your answer. · Lines g and h are positioned with line g above line h. · Lines j and k are positioned diagonally with line j to the left of line k. · Four angles are formed when line j intersects with line h. · The angle in the upper right position at that intersection is labeled 1. · Four angles are formed when line k intersects with line h. · The angle in the upper left position at that intersection is labeled 2. (1 point) Responses j || k by the converse of the Same-Side Interior Angles Theorem. j || k by the converse of the Same-Side Interior Angles Theorem. j || k by the converse of the Alternate Interior Angles Theorem. j || k by the converse of the Alternate Interior Angles Theorem. g || h by the converse of the Alternate Interior Angles Theorem. g || h by the converse of the Alternate Interior Angles Theorem. g || h by the converse of the Same-Side Interior Angles Theorem.
The correct response is j || k by the converse of the Same-Side Interior Angles Theorem. In this case, lines j and k are positioned diagonally, with line j to the left of line k. When line j intersects with line h, it forms four angles, and the angle in the upper right position at that intersection is labeled 1. When line k intersects with line h, it also forms four angles, and the angle in the upper left position at that intersection is labeled 2. Since angles 1 and 2 are same-side interior angles, and we are given that m1 + m2 = 180, we can conclude that lines j and k are parallel by the converse of the Same-Side Interior Angles Theorem.
Find the value of x for which l is parallel to m. The diagram is not to scale. · Line l is drawn above line m. · A segment is drawn connecting line l to line m with a positive slope. · The acute angle formed by that segment and line m is labeled x degree-sign. · The acute angle formed by that segment and line l is labeled 28 degree-sign. · To the left of the other segment, a segment is drawn connecting line l to line m with a negative slope. · One of the angles formed at the intersection of these two segments is labeled 56 degree-sign. · This 56 degree-sign angle is not in the interior of any triangle formed by the two segments. (1 point) Responses 28 28 56 56 84 84 152
To find the value of x for which line l is parallel to line m, we need to use the property that when two parallel lines are intersected by a transversal, the corresponding angles are congruent.
From the given information, we know that the acute angle formed by the segment connecting line l to line m and line m is labeled x degrees. We also know that the acute angle formed by the segment connecting line l to line m and line l is labeled 28 degrees.
Since line l is parallel to line m, the angle labeled 28 degrees is a corresponding angle to the angle labeled x degrees. Therefore, we can set up the equation:
28 degrees = x degrees
Solving for x, we find that x = 28 degrees.
To determine which lines are parallel, given the condition that m1 + m2 = 180:
- The lines j and k are positioned diagonally, with line j to the left of line k. When line j intersects with line h, four angles are formed. The angle in the upper right position at that intersection is labeled 1.
- Similarly, when line k intersects with line h, four angles are formed. The angle in the upper left position at that intersection is labeled 2.
To determine which lines are parallel, we can use the converse of the Same-Side Interior Angles Theorem or the converse of the Alternate Interior Angles Theorem.
Based on the information provided, it can be justified that j and k are parallel lines using the converse of the Alternate Interior Angles Theorem. Therefore, the correct response is:
j || k by the converse of the Alternate Interior Angles Theorem.
To determine which lines are parallel, we can use the converse of the Same-Side Interior Angles Theorem and the converse of the Alternate Interior Angles Theorem.
First, let's analyze the given information step by step:
1. Lines g and h are positioned with line g above line h.
2. Lines j and k are positioned diagonally with line j to the left of line k.
3. Four angles are formed when line j intersects with line h.
4. The angle in the upper right position at that intersection is labeled 1.
5. Four angles are formed when line k intersects with line h.
6. The angle in the upper left position at that intersection is labeled 2.
Now, let's apply the theorems:
The Same-Side Interior Angles Theorem states that if a pair of lines is cut by a transversal and the sum of two interior angles on the same side of the transversal is 180 degrees, then the lines are parallel.
The Alternate Interior Angles Theorem states that if a pair of lines is cut by a transversal and two alternate interior angles are congruent, then the lines are parallel.
Based on the given information:
- We are given that the angle in the upper right position at the intersection of line j and line h is labeled 1, and the angle in the upper left position at the intersection of line k and line h is labeled 2.
To apply the theorems, we need to determine if the sum of angles 1 and 2 equals 180 degrees:
- If the sum of angles 1 and 2 is equal to 180 degrees, then lines j and k are parallel by the converse of the Same-Side Interior Angles Theorem.
- If angles 1 and 2 are congruent, then lines j and k are parallel by the converse of the Alternate Interior Angles Theorem.
Unfortunately, the information provided does not allow us to determine the values or relationships between angles 1 and 2. Therefore, we cannot determine if lines j and k are parallel or not.
As for lines g and h, we do not have enough information to determine their parallelism. The given information only establishes their relative positions, and we cannot make any conclusions about their parallelism.
In conclusion, based on the given information, we cannot determine which lines are parallel using the theorems mentioned.