Respuesta :

Solution:

Note that:

  • Opposite angles are always equal.
  • The sum of the degrees in a quadrilateral is 360°

This means that:

  • ∠F = ∠D = 62°
  • ∠E = ∠G = 5p + 49
  • ∠F + ∠D + ∠E + ∠G = 360

Solving for p.

  • ∠F + ∠D + ∠E + ∠G = 360
  • => 62 + 62 + 5p + 49 + 5p + 49 = 360
  • => p(5 + 5) + (62 + 62 + 49 + 49) = 360
  • => p(10) + (222) = 360
  • => 10p + 222 = 360
  • => 10p = 360 - 222
  • => 10p = 138
  • => 10p/10 = 138/10
  • => p = 13.8

Check:

  • ∠E = ∠G = 5p + 49
  • => ∠E = ∠G = 5(13.8) + 49
  • => ∠E = ∠G = 69 + 49
  • => ∠E = ∠G = 118°
  • => ∠F + ∠D + ∠E + ∠G = 360
  • => 62 + 62 + 118 + 118 = 360
  • => 360 = 360 (True)

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