Question

Help, Parallelogram JKLM is shown.

What is m
What is JR?

Answer 1

First answer is 22

Second answer is 7

Before I explain the answer, first visualize triangle KJM

angle MKJ is congruent to angle JMR by alternate interior angles, Note how we have 2 angles measures for triangle MKJ.

Next solve for angle KJM using angle sum theorem (all angles in a triangle must equal 180)

72+27+x= 180

x=81

We now know that angle KJM is 81 however the question ask for the other angle created the line segment.

angle KJM - angle KJL

81-56 = angle LJM

22 = angle LJM

Second question

If you know the properties of a parallelogram you should know that its vertices are congruent to itself.

First you solve for x

x+7 = 3x -5

7=2x -5

12=2x

12/2=x

6=x

Next find the value of JL by plugging in the x values

4(6) - 10 = JL

24 - 10 = JL

14 = JL

Finally you divide line JL by half, since line JR and RL and congruent

14/2=JR

7=JR

Cheers