Question

In the figure m21 = 17 + 5x and m22 = 7x-25. Find value of x. Explain

Answer 1

• 
  `\sf x = 21`
• 
  `\sf m\angle1 = 122\degree`
• 
  `\sf m \angle2 = 122\degree`
• 
  `\sf m\angle3 = 122\degree`

Step-by-step Step-by-step explanation:

`\sf m \angle 1` and
`\sf m \angle2` are the alternate interior angles.

Alternate angles are the pair of angles that are formed on the opposite side of the transversal line and are always equal.

hence,
`\sf m\angle1 = m\angle2`

`\sf 17 + 5x = 7x - 25`

subtracting 17 from both sides

`\sf 17 + 5x - 17 = 7x - 25 - 17`

`\sf 5x = 7x - 42`

subtracting 7x from both sides

`\sf 5x - 7x = -42`

`\sf -2x = -42`

dividing both sides by -2

`\sf (-2x)/(2) = (-42)/(-2)`

`{\boxed{\bf{x = 21}}}`

therefore, x = 21

now,

`\sf m \angle1 = 17 + 5x`

plugging the value of x

`\sf m\angle1 = 17 + 5(21)`

`\sf m\angle1 = 17 + 105`

`{\boxed{\bf {m\angle1 = 122\degree}}}`

and,

`\sf m\angle 2 = 7x - 25`

`\sf m \angle2 = 7(21) - 25`

`\sf m \angle2 = 147 - 25`

`{\boxed{\bf {m \angle2 = 122\degree}}}`

also,
`\sf m\angle2` and
`\sf m\angle3` are the vertical opposite angles, they are congruent i.e measures equal

`{\boxed{\bf{ m\angle3 = 122\degree}}}`