Answer:

Explanation:
The given diagram shows a circle with two secants drawn to the circle from one exterior point. The angle formed by the two secants is x°. The two intercepted arcs are 164° and 40°.
To find the value of x, we can use the Intersecting Secants Theorem.
Intersecting Secants Theorem
If two secant segments are drawn to the circle from one exterior point, the measure of the angle formed by the two lines is half of the (positive) difference of the measures of the intercepted arcs.
Therefore, according to the Intersecting Secants Theorem:

Solving the equation for x:



Therefore, the value of x is 62.