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Mathematics

1 answer:

tekilochka [14]3 years ago

5 0

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

∠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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