To get the amount of degrees altogether in the polygon, you can use the equation of 180 x ( n - 2 ) to get the total number, where n = total sides.
In this case, the equation reads 180 ( 6 - 2 )
180 x 4 = 720
There are 720 degrees altogether in the polygon.
To get a, you can take the total amount of degrees and subtract all the other degrees to get angle a.
Since there is one angle missing, the one around the right angle, you can calculate it by doing 360 - 90 = 270.
There are angles a, 130, 80, 40, and 270 in the polygon.
Now you can subtract them all:
a = 720 - 270 - 130 - 80 - 40 - x
a = 200 - x
Now to get x which is the final angle missing with nothing labelled, you can use the parallelogram thereom with angle 80, the alternative angles. You can do 180 - 80 to get angle x, which x will equal 100.
Now you can get angle a:
a = 200 - 100
a = 100
angle A = 100
*assume each number has a degree on it*
