Answer:
D. [tex]60^o[/tex]
Step-by-step explanation:
We have been given a diagram of circle and we are asked to find the value of x.
We can see from our diagram that it has a angle formed by a secant and tangent of the circle which measure 55 degrees.
Since the tangent-secant angle theorem states that the angle formed by a secant and tangent outside the circle is the half the difference of measures of its intercepted arcs (major arc-minor arc).
We can see that measure of Tangent-Secant angle is 55 degrees. Major arc intercepting to the angle has a measure of 170 degrees and minor arc measures x degrees.
Using our given information we can set an equation as:
[tex]55^o=\frac{170^o-x^o}{2}[/tex]
Now let us solve for x by multiplying both sides of our equation by 2.
[tex]55^o*2=\frac{170^o-x^o}{2}*2[/tex]
[tex]110^o=170^o-x^o[/tex]
Now let us subtract 170 degrees from both sides of our equation.
[tex]110^o-170^o=170^o-170^o-x^o[/tex]
[tex]110^o-170^o=-x^o[/tex]
[tex]-60^o=-x^o[/tex]
[tex]60^o=x^o[/tex]
Therefore, value of x is 60 degrees and option D is the correct choice.
