#1) Since ∠O = 136°, the intercepted arc is also 136°. This means the other arc is 360-136=224°. The measure of an angle formed by two tangents is half of the difference of the intercepted arcs; this is 1/2(224-136) = 1/2(88) = 44°.
#2) Point Q is tangent to the circle, and forms a 90° angle with the radius at that point. Point P = 16°. The three angles together form a triangle, which has a sum of 180°. This means the missing angle is equal to 180-(90+16) = 180-106 = 74°.
