Respuesta :

fieryanswererft

Answer:

m∠6 = 54°

Explanation:

m∠6 = (5x + 9)

m∠2 = 180 - (13x + 9)

As we can see m∠2 = m∠6 as corresponding angles.

5x + 9 = 180 - (13x + 9)

5x + 9 = 180 - 9 - 13x

5x + 13x = 180 - 9 - 9

18x = 162

x = 9

So, m∠6 = 5x + 9 = 5(9) + 9 = 45 + 9 = 54

MisterBrian

Answer:

m<6 = 54°

Step-by-step explanation:

Given:

  • b || c

Here, (13x+9)° and <6 are vertically opposite on each side.So,they are equal.

  • 13x+9 = <4

By alternate angle theorem,4 and 5 makes "Z" angle on each side, where a is the transversal,so they are equal.

  • <4 = <5 = (13x+9)°

By linear pair theorem,on a straight line, two angles formed by a transversal cutting the line in two parts' sum equals to 180°.

  • Here, <5 and (5x+9)° addition makes 180°

But <5 = (13x+9)°

So:

  • <5 + (5x+9)° = 180
  • (13x+9)° + (5x+9)° = 180

Solve for x now:

  • 18x +18 = 180 ... Combine terms
  • 18(x+1) = 180 ... Take 18 common
  • x+1 = 180/18 ... Divide both sides by 18
  • x = 10 -1 = 9 ... Subtract 1 from both sides

We're required to find <6,i.e (5x+9)°[See above]

  • m<6 = 5*9 + 9 = 45+9 = 54°

Otras preguntas