Respuesta :

Hrishii

Answer:

[tex]{\purple{ \bold{m\angle 1=164\degree}}}[/tex]

Step-by-step explanation:

  • Given figure is of a parallelogram.

  • [tex]m\angle 2 = 4x - 20[/tex] (Given)

  • [tex]m\angle 4 = 3x - 11[/tex] (Given)

  • [tex]\angle 2\:\&\: \angle 4\:[/tex] are opposite angles of a parallelogram.

  • Measures of opposite angles of a parallelogram are equal.

  • [tex]\implies m\angle 2=m\angle 4[/tex]

  • [tex]\implies 4x-20=3x-11[/tex]

  • [tex]\implies 4x -3x = 20-11[/tex]

  • [tex]\implies\red{\bold{ x = 9}}[/tex]

  • [tex]\implies m\angle 2 = (4*9 - 20)\degree= (36 - 20)\degree[/tex]

  • [tex]\implies m\angle 2 =16\degree[/tex]

  • [tex]\angle 1\:\&\: \angle 2\:[/tex] are consecutive angles of a parallelogram.

  • Consecutive angles of a parallelogram are supplementay.

  • [tex]\implies m\angle 1+m\angle 2=180\degree[/tex]

  • [tex]\implies m\angle 1+16\degree=180\degree[/tex]

  • [tex]\implies m\angle 1=180\degree-16\degree[/tex]

  • [tex]\implies\huge{\orange{ m\angle 1=164\degree}}[/tex]

Otras preguntas