Question

If RS=59 AND ST=10x-31,find x

Answer 1

RS is the length of segment RS, not the length of arc RS.

ST is the length of segment ST, not arc ST.

The arcs RS and ST have little marks in the picture. These marks indicate that the arcs are congruent. They have the same length. In a circle, or in congruent circles, congruent arcs are intercepted by congruent chords.

This means that segments RS and ST are congruent.

ST = RS

10x - 31 = 59

10x = 90

x = 9

Answer 2

Answer: x=9

Step-by-step explanation:

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

And $\overline{RS}=59\text{ and }\overline{ST}=10x-31$

Since, we know that congruent arcs have congruent chords.

Therefore,  $\overline{RS}=\overline{ST}$

$59=10x-31\\\\\Rightarrow\ 10x=59+31\\\\\Rightarrow 10x=90\\\\\Rightarrow x=\frac{90}{10}\\\\\Rightarrow x=9$