Answer:
x = 24
Explanation:
You want the value of x in a geometry showing a major arc of (14x -22)° and a minor arc subtended by an inscribed angle of 23°.
Minor arc
The measure of the minor arc subtended by the secant is double the measure of the angle between the secant and tangent. It is 2·23° = 46°.
Major arc
The sum of arcs in a circle is 360°, so the major arc is ...
360° -46° = 314°
This arc is labeled (14x -22)°, so we have the equation ...
314° = (14x -22)°
336 = 14x . . . . . . . . . divide by °, add 22
24 = x . . . . . . . . . . divide by 14
The value of x is 24.