Answer:
[tex]x=58[/tex]
Step-by-step explanation:
We have been given an image of a circle. We are asked to find the value of x.
We can see that angle that measure 51 degrees is formed by tangent and secant of our given circle.
The tangent-secant theorem of circle states that when a secant and tangent intersect out side the circle, then the measure of angle formed is half the difference of intercepted arcs.
[tex]51^{\circ}=\frac{160^{\circ}-x^{\circ}}{2}[/tex]
[tex]51^{\circ}*2=\frac{160^{\circ}-x^{\circ}}{2}*2[/tex]
[tex]102^{\circ}=160^{\circ}-x^{\circ}[/tex]
[tex]102^{\circ}-160^{\circ}=160^{\circ}-160^{\circ}-x^{\circ}[/tex]
[tex]-58^{\circ}=-x^{\circ}[/tex]
[tex]x=58[/tex]
Therefore, the value of x is 58.
