We need to compute all the interior angles first.

I will do this in an anticlockwise order, starting with the interior angle in between the yellow 80 and the red x.

Interior angle 1
= 180 - 80 - x
= 100 - x

Next, the one directly below it.

Interior angle 2
= 180 - x

Next, the 125.

Next, the one next to the purple 2x.

Interior angle 3
= 180 - 2x

The remaining three interior angles (I cut my workings short) are 180 - x, 180 - x and 180 - 3x.

Sum of all seven interior angles
= (100 - x) + (180 - x) + 125 + (180 - 2x) + (180 - x) + (180 - x) + (180 - 3x)
= 1125 - 9x

Since this is a seven-sided polygon, total sum of interior angles
= 180 (7 - 2)
= 900

So,

1125 - 9x = 900
-9x = -225
x = 25

It will be easier to use sum of exterior angles of a polygon = 360° here.


For the yellow 80° and x at the top left corner, the lines of either side of that angle can be extended such that we have vertically opposite angles.

Then we realise that this exterior angle is just 80° + x

(Or you can think of it as rotating the external line to match either side, and by doing this, we will have added x to the 80° or 80° to the x)

The exterior angle next to the 125° would simply be 180° - 125° = 55°

Adding them altogether,

80° + x + x + 55° + x + x + 2x + 3x = 360°
9x + 135° = 360°
9x = 225°
x = 25°