Respuesta :

mhanifa

Answer:

90°

Step-by-step explanation:

AB and  CD are parallel lines and EF is reversal

Therefore angles BGH and DHG are consecutive interior angles

As we know the sum of consecutive interior angles equals to 180°:

  • ∠BGH + ∠DHG = 180°

Line GP bisects angle BGH , therefore

  • m∠PGH = 1/2*m∠BGH

Line HP bisects angle GHD, therefore

  • m∠PHG = 1/2*m∠GHD

Sum of two angles of triangle GHP:

  • m∠PGH + m∠GHD = 1/2(∠BGH + ∠DHG) = 1/2*180° = 90°

Therefore the missing angle a is:

  • ∠a = 180° - (m∠PGH + m∠GHD) = 180° - 90° = 90°

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