Find the length of side x in simplest radical form with a rational denominator

What are the values of m∠abc, m∠cbf, m∠abd and m∠dbe in the given figure? explain or show your work?

Both the red and blue line segments stretch from the center of the circle to a point on the circle. the length of the blue segment is 5. how long is the red line segment?

Corresponding angles are a. always b. sometimes c. never congruent