maxlarson
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Sagot :

mhanifa

Answer:

  • JR = 29
  • ∠JLM = 25°

Step-by-step 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°
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