Respuesta :

JeanaShupp

Answer: x=9

Step-by-step explanation:

In the given picture, we have a circle in which we have given two congruent arcs [tex]\overarc{RS}\text{ and }\overarc{TS}[/tex]

And [tex]\overline{RS}=59\text{ and }\overline{ST}=10x-31[/tex]

Since, we know that congruent arcs have congruent chords.

Therefore,  [tex]\overline{RS}=\overline{ST}[/tex]

[tex]59=10x-31\\\\\Rightarrow\ 10x=59+31\\\\\Rightarrow 10x=90\\\\\Rightarrow x=\frac{90}{10}\\\\\Rightarrow x=9[/tex]

To solve the problem we must know the Chord's Equidistant From The Center Of A Circle Theorem.

Equidistance chords

If two chords of a circle are equidistant from the center then they are congruent to each other and their corresponding arcs are also congruent.

The value of x is 9.

Given to us

  • RS = 59,
  • ST = 10x-31,

In circle,

Chord RS and chord ST are equidistant from the center. therefore,

RS = ST

[tex]59 = 10x-31\\ 59+31 = 10x\\ 90 = 10x\\\\ x= \dfrac{90}{10}\\\\ x= 9[/tex]

Hence, the value of x is 9.

Learn more about Equidistance chords:

https://brainly.com/question/2364467

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