Question

What is the value of x?

Answer 1

51= 1/2(160-x)
102=160-x
x=160-102=58

Answer 2

`x=58`

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.

`51^(\circ)=(160^(\circ)-x^(\circ))/(2)`

`51^(\circ)*2=(160^(\circ)-x^(\circ))/(2)*2`

`102^(\circ)=160^(\circ)-x^(\circ)`

`102^(\circ)-160^(\circ)=160^(\circ)-160^(\circ)-x^(\circ)`

`-58^(\circ)=-x^(\circ)`

`x=58`

Therefore, the value of x is 58.