1. The angle formed by a tangent and a secant outside a circle is half the difference of the intercepted arcs. Here, arcs are 200° and 220°. $$x=\frac{|220-200|}{2}=\frac{20}{2}=10^\circ$$ 2. Arcs are 70° and 65°. $$x=\frac{|70-65|}{2}=\frac{5}{2}=2.5^\circ$$ 3. Arcs are 65° and 190°. $$x=\frac{|190-65|}{2}=\frac{125}{2}=62.5^\circ$$ 4. Arcs are 80° and 225°. $$x=\frac{|225-80|}{2}=\frac{145}{2}=72.5^\circ$$ 5. Arcs are 216° and 72°. $$x=\frac{|216-72|}{2}=\frac{144}{2}=72^\circ$$ 6. For interior angle formed by intersecting chords, measure is half sum of intercepted arcs: 60° and 48°. $$x=\frac{60+48}{2} = \frac{108}{2} = 54^\circ$$ 7. Interior angle x with arcs 45° and 65°, segment y between them means $$x=\frac{45+65}{2}=\frac{110}{2}=55^\circ$$ 8. Exterior angle x, arcs 60°, 85° $$x=\frac{|85-60|}{2}=\frac{25}{2}=12.5^\circ$$ 9. Interior angle x with arc 125° and segment y (no second arc given). Usually, angle formed by chords is half sum of arcs. Since second arc missing, cannot solve x exactly without more info. 10. With chords intersecting inside the circle creating angle x and arcs 216° and 50°. $$x=\frac{216+50}{2}=\frac{266}{2}=133^\circ$$ Final answers: 1. $10^\circ$ 2. $2.5^\circ$ 3. $62.5^\circ$ 4. $72.5^\circ$ 5. $72^\circ$ 6. $54^\circ$ 7. $55^\circ$ 8. $12.5^\circ$ 9. Insufficient information 10. $133^\circ$