Question

Find the value of x.

69
57
63
60​

Answer 1

D.
`60^o`

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:

`55^o=(170^o-x^o)/(2)`

Now let us solve for x by multiplying both sides of our equation by 2.

`55^o*2=(170^o-x^o)/(2)*2`

`110^o=170^o-x^o`

Now let us subtract 170 degrees from both sides of our equation.

`110^o-170^o=170^o-170^o-x^o`

`110^o-170^o=-x^o`

`-60^o=-x^o`

`60^o=x^o`

Therefore, value of x is 60 degrees and option D is the correct choice.