Question

Please explain steps and the answer! No answer choices.

Answer 1

`{\purple{ \bold{m\angle 1=164\degree}}}`

Explanation:

• Given figure is of a parallelogram.

• 
  `m\angle 2 = 4x - 20` (Given)

• 
  `m\angle 4 = 3x - 11` (Given)

• 
  `\angle 2\:\&\: \angle 4\:` are opposite angles of a parallelogram.

• Measures of opposite angles of a parallelogram are equal.

• 
  `\implies m\angle 2=m\angle 4`

• 
  `\implies 4x-20=3x-11`

• 
  `\implies 4x -3x = 20-11`

• 
  `\implies\red{\bold{ x = 9}}`

• 
  `\implies m\angle 2 = (4*9 - 20)\degree= (36 - 20)\degree`

• 
  `\implies m\angle 2 =16\degree`

• 
  `\angle 1\:\&\: \angle 2\:` are consecutive angles of a parallelogram.

• Consecutive angles of a parallelogram are supplementay.

• 
  `\implies m\angle 1+m\angle 2=180\degree`

• 
  `\implies m\angle 1+16\degree=180\degree`

• 
  `\implies m\angle 1=180\degree-16\degree`

• 
  `\implies\huge{\orange{ m\angle 1=164\degree}}`