The shape that is shown in the image is a heptagon (it has 7 sides), to determine the sum of the interior angles of any shape you have to subtract 2 to the number of sides of the shape and multiply the result by 180. The formula is as follows:
[tex](n-2)\cdot180[/tex]
Where n represents the number of sides.
The sides on the heptagon are n=7, replace this value in the formula and you get the sum of the inner angles of the shape:
[tex](7-2)\cdot180=5\cdot180=900º[/tex]
The sum of the interior angles of the heptagon is 900º
Now that you know how much do the interior angles add up to we can calculate the value of x as follows:
[tex]\angle D+\angle E+\angle F+\angle G+\angle H+\angle J+\angle K=900º[/tex]
Replace the expression with the known measures of all angles and calculate for the missing one
[tex]\begin{gathered} 110+135+147+128+118+135+x=900 \\ 773+x=900 \\ 773-773+x=900-773 \\ x=127º \end{gathered}[/tex]
The value of x is 127º
