Allan2006 Allan2006
  • 15-09-2020
  • Mathematics
contestada

wxyz-параллелограмм. Найдите углы угол W, угол X, угол Y и угол Z

wxyzпараллелограмм Найдите углы угол W угол X угол Y и угол Z class=

Respuesta :

eudora eudora
  • 20-09-2020

Answer:

∠W = 115°

∠X = 65°

∠Y = 115°

∠Z = 65°

Step-by-step explanation:

From the picture attached,

Since, sides WX and YZ are parallel and WZ is a transversal,

m∠W + m∠Z = 180° [Sum of consecutive interior angles]

(18b - 11) + (9b + 2) = 180°

27b - 9 = 180°

27b = 189

b = [tex]\frac{189}{27}[/tex]

b = 7

m∠W = (18b - 11)° = 115°

m∠Z = (9b + 2)° = 65°

Since, m∠Z = m∠X and m∠W = m∠Y [Property of the angles of a parallelogram]

m∠Z = m∠X = 65°

m∠W = m∠Y = 115°

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