To solve for [tex]\( x \)[/tex] given that a pentagon has angles [tex]\( x^\circ, 2x^\circ, (x+60)^\circ, (x+10)^\circ \)[/tex], and [tex]\( (x-10)^\circ \)[/tex], we need to use the fact that the sum of the interior angles of a pentagon is always 540 degrees.
Step-by-step solution:
1. Identify the angles:
The angles given are:
- [tex]\( x \)[/tex]
- [tex]\( 2x \)[/tex]
- [tex]\( x + 60 \)[/tex]
- [tex]\( x + 10 \)[/tex]
- [tex]\( x - 10 \)[/tex]
2. Write the equation for the sum of the interior angles:
The sum of the interior angles of a pentagon is 540 degrees. Therefore, we can write the equation:
[tex]\[
x + 2x + (x + 60) + (x + 10) + (x - 10) = 540
\][/tex]
3. Combine like terms:
Combine all the terms involving [tex]\( x \)[/tex]:
[tex]\[
x + 2x + x + x + x + 60 + 10 - 10 = 540
\][/tex]
Simplify it further:
[tex]\[
6x + 60 = 540
\][/tex]
4. Solve for [tex]\( x \)[/tex]:
Subtract 60 from both sides of the equation:
[tex]\[
6x = 480
\][/tex]
Divide both sides by 6:
[tex]\[
x = 80
\][/tex]
So, the value of [tex]\( x \)[/tex] is [tex]\(\boxed{80}\)[/tex].
