10. from the question; the circle theorem obeyed is "angled formed by semi-circle"
The angle formed in a semicircle is 90 degrees, hence

This gives

But

Substituting values we get

hence, x =12
180 - 53 - 96 = 31°. you know the angles are 53 and 96 degrees because the triangles are congruent via SAS congruency.
Answer:
Initial equation: 5x + 2 = 3x + 12
x = 5
Step-by-step explanation:
Point C is the midpoint between A and B.
This means that:
AC = CB
We have that:
AC = 5x + 2
CB = 3x + 12
Since AC = CB, the initial equation is:
5x + 2 = 3x + 12
Now we can solve
5x + 2 = 3x + 12
5x - 3x = 12 - 2
2x = 10
x = 10/2
x = 5