Respuesta :

xero099

The missing measures are listed below:

  1. [tex]m \angle 1 = m \angle 3 = m \angle 6 = 59^{\circ}[/tex]
  2. [tex]m\angle 2 = m\angle 4 = m\angle 5 = m \angle 11 = 31^{\circ}[/tex]
  3. [tex]m\angle 7 = m\angle 8 = m\angle 9 = m\angle 10 = 118^{\circ}[/tex]

Procedure - Finding missing angles in a quadrilateral

In this question we must determine the measures of the missing angles by both geometric and algebraic means, whose procedure is presented below:

  1. [tex]x = 59^{\circ}[/tex] Given
  2. [tex]m \angle 3 = 59^{\circ}[/tex] Alternate internal angles
  3. [tex]m \angle 11 = 31^{\circ}[/tex] Complementary angles
  4. [tex]m \angle 4 = 31^{\circ}[/tex] Alternate internal angles
  5. [tex]m \angle 6 = 59^{\circ}[/tex] Isosceles triangle
  6. [tex]m \angle 9 = 62^{\circ}[/tex] Sum of internal angles in a triangle
  7. [tex]m \angle 10 = 118^{\circ}[/tex] Supplementary angles
  8. [tex]m \angle 8 = 62^{\circ}[/tex], [tex]m\angle 7 = 118^{\circ}[/tex] Vertical angles
  9. [tex]m \angle 2 = 31^{\circ}[/tex] Sum of internal angles in a triangle
  10. [tex]m \angle 5 = 31^{\circ}[/tex] Sum of internal angles in a triangle
  11. [tex]m \angle 1 = 59^{\circ}[/tex] Sum of internal angles in a triangle/Result

The missing measures are listed below:

  1. [tex]m \angle 1 = m \angle 3 = m \angle 6 = 59^{\circ}[/tex]
  2. [tex]m\angle 2 = m\angle 4 = m\angle 5 = m \angle 11 = 31^{\circ}[/tex]
  3. [tex]m\angle 7 = m\angle 8 = m\angle 9 = m\angle 10 = 118^{\circ}[/tex]

To learn more on angles, we kindly invite to check this verified question: https://brainly.com/question/15767203

Otras preguntas