check the picture below.
recall that all interior angles in a triangle, add up to 180°.
how did we get angle 21? well, 180 - 90 - 55.
and angle 23 is a vertical angle of 21, thus equal.
now, a circle has a total of 360°, so, if we take out angles 21 and 23, so 70° from 360°, we're left with 290°, two equal, vertical, angles for 290° will be 145° each, thus angle 22 is 145°.
how did we get say angle 7? well, angle 7 is corresponding angle to angle 3, and thus equals.
how did we get angle 6? well, 180 - 70 - 90.