Answer:
x = 12.5
Step-by-step explanation:
Since measure of 4th arc is not given (measure of 3 arcs have been given), we will apply the following theorem.
By the intersecting chords theorem,
"If two chords intersecting inside a circle, measure of the angle between these chords will measure the half the sum of measures of arcs intercepted by the angle and its vertical angle."
Here intercepted arcs are (2x)° and 155°. Angel between the chords measure 90°.
By the theorem,
90° = [tex]\frac{1}{2}(2x + 155)[/tex]°
180° = (2x + 155)°
2x = 180 - 155
2x = 25
x = 12.5
