1) x = 73 degrees
If arc AC is 128 degrees, then angle B is going to be half of that. Inscribed angles are 1/2 of the measure of their corresponding arc. Therefore, angle B is 64 degrees.
The sum of the interior angles of a triangle is 180 degrees. We know 2 of the interior angles and can very easily solve for the third.
43 + 64 + x = 180
107 + x = 180
x = 73
2) x = 7
Since these chords intersect, the product of the segments of each chord will be the same.
KH * HI = JH * HG
10 * x = 14 * 5
10x = 70
x = 7
Hope this helps!