Which lines are parallel if mangle1 + mangle2 = 180? Justify your answer.
An image showing four intersecting lines and four intersection points is shown.· 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 answer is:
g || h by the converse of the Alternate Interior Angles Theorem.
If the sum of two angles formed by a transversal line intersecting two other lines is 180 degrees, then the two other lines are parallel. In this case, angles 1 and 2 are formed by the transversal line intersecting lines j and h or k and h. Since angle 1 + angle 2 = 180 degrees, we can conclude that lines j and k or lines g and h are parallel. However, we cannot determine the parallel lines based on the given information.