Find the measures of each angle in the triangle.

We use 2 different rules here:

1) sum of angles in a triangle is equal to 180 degrees

2) when a triangle side is a diameter of the circle, then angle opposite to diameter is equal to 90 degrees.

so from 2) we know that B= 90

then from first one:

sum of angles = 180 = 90 + (3x + 6) + x = 96 + 4x

so 180 - 96 = 4x
so x = 84/4
x = 21

so answer is
A= 3x+ 6 = 63 + 6 = 69
B = 90
C = 21