Answer:
The value of x is 11.5.
Step-by-step explanation:
Since, when one tangent and one secant intersect outside a circle, then the measure of the intersection angle is half of the difference of the intercepted arcs,
In the given diagram,
AD is the secant and AC is the tangent of the circle,
Also, AD and AC intersect at A,
Thus, by the above statement,
[tex]m\angle A=\frac{m\widehat{DC}-m\widehat{BC}}{2}[/tex]
Here,
[tex]m\angle A=12^{\circ}[/tex]
[tex]m\widehat{DC}=4x-2[/tex]
[tex]m\widehat{BC}=20^{\circ}[/tex]
[tex]\implies 12=\frac{4x-2-20}{2}[/tex]
[tex]24=4x-22[/tex]
[tex]46=4x[/tex]
[tex]\implies x=11.5[/tex]
