what is the value of x in the concave polygon below?

Question

I know that the value of $x$ in this problem is 169 by exterior angle sum theorem (I extended the dashed line with the 58° angle to create a triangle). But I have to fill in this equation to solve for $x$. I just don't know how to come with that equation.

$x-(...)+(...)+(...)=(...)$

Answer 1

Trace the polygon going anti-clockwise. The sum of the angles through which you turn to get back to your starting point and starting direction should be $360^{\circ}$. Where you turn anti-clockwise the angles are positive. Where you turn clockwise from one side to the next these angles are negative.

Starting at the top left vertex and heading approx. south : $$(+x)+(-58)+(+158)+(+91)=360$$

Answer 2

Draw the red line as shown.

By 'exterior angle of triangle', x = p + q = (r + s) + q

Start replacing q, r , and s by suitable numbers.

Re-arrange terms to make an equation that has the required form.