Respuesta :

roohafzah

Answer :

  • θ = 52°

Explanation :

In Δ XBC,

  • m∠CXB = m∠B ( base angles of isosceles triangle are equal in measure )

thus,

  • m∠CXB + m∠B + m∠C = 180°
  • m∠CXB + m∠CXB + 58° = 180°
  • 2m∠CXB + 58° = 180°
  • 2m∠CXB = 180° - 58°
  • 2m∠CXB = 122°
  • m∠CXB = 122°/2
  • m∠CXB = 61°

In line AB ,

  • m∠AXY + m∠YXC + m∠CXB = 180° ( measure of a straight line is equal to 180° )
  • 67° + θ + 61° = 180°
  • θ + 128° = 180°
  • θ = 180° - 128°
  • θ = 52°
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