Question

20 points!

Answer 1

Short Answer x = 22 or C
The chord running through C is the circle's diameter. The angle opposite that diameter is a right angle. Any point on the circumference of a circle will make a right angle with  the two end points of the diameter except the two end points of the diameter. 

So the fact you should use is that the three angles of the triangle make 180 degrees (all triangles have 180 degrees). 

In this case you know two of the angles 
68o is one of them
90o is the other angle
x makes the third angle of the triangle.

x + 68 + 90 = 180      Combine like terms.
x + 158 = 180            Subtract 158 from both sides.
x = 180 - 158
x = 22 degrees <<<< Answer.