Question

Prove: A vertical line spans from point J to K has a midpoint L. Point L left side has a straight line to point M by the linear pair theorem, angle LMK is supplementary to ___.

A) Angle JMK
B) Angle LJK
C) Angle JKL
D) Angle KJM

Answer 1

To prove that angle LMK is supplementary to angle LJK, we can apply the linear pair theorem. A vertical line with midpoint L will have equal angles on either side, and since LMK is a straight line, it will be supplementary to LJK.

Step-by-step explanation:

To prove that angle LMK is supplementary to angle LJK, we need to apply the linear pair theorem. The linear pair theorem states that if two angles form a straight line, then they are supplementary (their sum is equal to 180 degrees).

1. From the given information, we know that a vertical line spans from point J to K and has a midpoint L.
2. Since L is the midpoint of the line, JL and LK are equal in length.
3. Therefore, angle LJK and angle LKJ are equal in measure (since they are opposite angles formed by the intersection of two lines).
4. Since LMK is a straight line and angle LKJ and angle LMK are adjacent angles, they form a straight line and are therefore supplementary.

Therefore, angle LMK is supplementary to angle LJK (which corresponds to option C).