Question

This is another 2 step. Please be sure to answer the question fully and show all of your work! I don't like reporting people.

Answer 1

• JR = 29
• ∠JLM = 25°

Explanation:

Diagonals of the parallelogram bisect each other

Note. The first question is repeated as A and B

A) KR = 1/2KM

Substitute and solve for x:

• x + 7 = 1/2(3x - 5)
• 2x + 14 = 3x - 5
• 3x - 2x = 14 + 5
• x = 19

Find JR

• JR = 1/2JL
• JR = 1/2(4x - 10) = 2x - 5 = 2*19 - 5 = 34 - 5 = 29

B)

• ∠LJM ≅ ∠JLK as alternate interior angles
• ∠JKL ≅ ∠JML as opposite angles of parallelogram

Interior angles of the triangle sum to 180°:

• m∠JLK + m∠LJK + m∠JKL = 180°
• m∠JLM = m∠JLK = 180° - (56° + 27° + 72°) = 25°