What is the dot on the line in #4. Is that line supposed to be a diameter?
The formula you are looking for is that an angle whose vertex is on a circle that measures an arc has a measure of half the arc.
So the angle on the lower right measures an arc of 89 degrees, thus the angle is (1/2)*89 = 44.5 degrees.
The angle at the top of the triangle measures an arc of 180 degrees (since the chord it intesects is a diameter it measures half the circle) so the angle is (1/2)*180 = 90 degrees.
So your triangle has three angles: x, 44.5 degrees, and 90 degrees. The sum of the interior angles of a triangle has 180 degrees, so x = 180 - 44.5 - 90 = 45.5 degrees.