Respuesta :

mhanifa

Answer:

  • a) 36°, b) 36°, c) 72°

Step-by-step explanation:

Given:

  • PT║VW and SR is transversal
  • m∠PQR = 36°

To find:

  • a) m∠SQT
  • b) m∠QRW
  • c) m∠PRV

Solution

a) ∠SQT is vertical with ∠PQR and therefore has equal measure

  • m∠SQT = 36°

b) ∠QRW is corresponding angle with ∠SQT and therefore has equal measure

  • m∠QRW = 36°

c) m∠PRV = m∠PRQ as marked equal

  • m∠PRV +m∠PRQ + m∠QRW = 180° as straight angle
  • m∠PRV*2 = 180° - 36°
  • m∠PRV*2 =144°
  • m∠PRV = 144°/2
  • m∠PRV = 72°

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