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

Mathematics

2 answers:

Paha777 [63]3 years ago

4 0

Answer:

x=14

PN=MN=85

Step-by-step 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

marissa [1.9K]3 years ago

4 0

Answer:

<h2> $\huge \: x = 14 \:and\: \small\\ the\: length\: of\: the\: segment\: is \:85$ </h2>

Step-by-step explanation:

<h3>to understand this</h3><h3>you need to know about:</h3>

triangles congruency
equation
PEMDAS

<h3>tips and formulas:</h3>

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

<h3>let's solve:</h3><h3> $step - 1 : define$ </h3>

$8 x- 27 = 6x + 1$

<h3> $step - 2 : solve$ </h3>

$add \: 27 \: to \: both \: sides \\ 8x - 27 + 27 = 6x + 1 + 27 \\ 8x = 6x + 28$
$cancel \: 6x \: from \: both \: sides \\ 8x - 6x = 6x - 6x + 28 \\ 8x = 28$
$divide \: both \: sides \: by \: 2 \\ \frac{2x}{2} = \frac{28}{2} \\ x = 14$

<h3>the length of the segment is</h3>

8x-27

8.14-27

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