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Aleksandr-060686 [28]
2 years ago
14

What is the length of MN ?

Mathematics
1 answer:
solniwko [45]2 years ago
4 0

Answer:

<u>C. 4</u>

Step-by-step explanation:

Using the Law of Sines,

  • sinA / a = sinB / b

<u>Here,</u>

  • A = 63°
  • a = x + 8
  • B = 63°
  • b = 3x

<u>Solving</u> :

  • sin63°/x + 8 = sin63°/3x
  • x + 8 = 3x
  • 2x = 8
  • x = 4
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m\angle M = (6x - 2)\degree  \\  \\ m\angle M = (6 \times 19- 2)\degree  \\  \\ m\angle M = (114- 2)\degree  \\  \\  m\angle M =112\degree  \\  \\ \because m\angle M + m\angle N = 180\degree  \\ (adjacent \: angles) \\  \\ \therefore m\angle N = 180\degree   - m\angle M \\  \\ \therefore m\angle N = 180\degree   - 112 \degree \\  \\ \therefore m \angle N = 68\degree

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