Given:
The angles of a polygon are (x + 70)°, x°, (x + 30)°, (2x)°, (2x)°, (2x - 10)°.
The number of sides is, n = 6.
The objective is to find the value of x.
The sum of the inner angles of a polygon is, 180(n-2)°.
Then, the value of x can be calculated as,
[tex]\begin{gathered} (x+70)+x+(x+30)+2x+2x+(2x-10)=180\cdot(n-2) \\ x+70+x+x+30+2x+2x+2x-10=180\cdot(6-2) \\ 9x+90=180\cdot(4) \\ 9x+90=720 \\ 9x=720-90 \\ 9x=630 \\ x=\frac{630}{9} \\ x=70 \end{gathered}[/tex]
Hence, the value of x is 70.
