The value of x is 16
The figure shows a polygon with extra projected lines showing its exterior angles.
A sketch of the polygon is shown below:
The polygon is shown in the above sketch.
Projections off the side of the polygon show the exterior angles.
The theorem we shall use to solve for x is:
The sum of the exterior angles of a polygon is 360 degrees.
[tex]\begin{gathered} (2x-5)^0+(3x+65)^0+(6x+12)^0+2x^0+5x^0=360^0 \\ 2x-5+3x+65+6x+12+2x+5x=360^0 \end{gathered}[/tex]
Now, we need to collect and add like terms.
[tex]\begin{gathered} 2x+3x+6x+2x+5x-5+65+12=360 \\ 18x+72=360 \\ \\ \text{subtract 72 from both sides} \\ 18x+72-72=360-72 \\ 18x=288 \\ \text{divide both sides by 18} \\ \\ x=\frac{288}{18} \\ x=16 \end{gathered}[/tex]
The value of x is 16
