Before we attempt to solve for x, let's focus on the inner triangle — the one that has one vertex on the center of the circle and two of its vertices on the circumference. Since two of its sides are radii of the circle, they are congruent. This means that the opposite angles are congruent.
m∠ O+ 56+ 56=180 ⇔ m∠ O= 68
Let's now focus on the outer triangle.
If a line is tangent to a circle, then the line is perpendicular to the radius at the point of tangency.
Finally, to find the value of x, we will use the Triangle Angle Sum Theorem one more time.
x+ 90+ 68=180 ⇔ x = 22
