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Pls help me answer this questsion ASAP-example-1

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In the rhombus shown here, the measures of J and K are in the ratio 3:7. What is the measure of JKM?

A. 27°

B. 54°

C. 63° ✓

  • we know that , Adjacent angles of a rhombus measure 180°
  • Let ∠J be 3x & ∠K be 7x as the ratio between them is 3:7
  • ∴ , 3x + 7x = 180°
  • 10x = 180°
  • x = 180°/10
  • x = 18°
  • ∵, ∠J = 3x = 3*18° = 54°
  • and, ∠K = 7x = 7*18° = 126°
  • since,∠JKM = ∠LKM and ∠JKM + ∠LKM = ∠K (the diagonal of a rhombus bisects the angle through which it passes)
  • so, ∠JKM = ∠K/2
  • ∵∠JKM = 126°/2
  • ∠JKM = 63°

D. 126°

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