Question

What is the value of x and the length of the segment?

Answer 1

`\huge \: x = 14 \:and\: \small\\ the\: length\: of\: the\: segment\: is \:85`

Explanation:

to understand this

you need to know about:

• triangles congruency
• equation
• PEMDAS

tips and formulas:

• when two triangles are congruent the included angles and sides of the triangles are equal
• PN=MN

let's solve:

`8 x- 27 = 6x + 1`

`step - 2 : solve`

1. 
   `add \: 27 \: to \: both \: sides \\ 8x - 27 + 27 = 6x + 1 + 27 \\ 8x = 6x + 28`
2. 
   `cancel \: 6x \: from \: both \: sides \\ 8x - 6x = 6x - 6x + 28 \\ 8x = 28`
3. 
   `divide \: both \: sides \: by \: 2 \\ (2x)/(2) = (28)/(2) \\ x = 14`

the length of the segment is

8x-27

8.14-27

85

Answer 2

x=14

PN=MN=85

Explanation:

It is an isosceles triangle because PQ=MQ and QN is perpendicular to PM. PN=MN

8x-27=6x+1

2x=28

x=14

PN=MN=85