Question

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.

Answer 1

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

Answer 2

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.

Answer 3

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.