Question

What is the value of x?

Answer 1

Answer:

$x=58$

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.

$51^{\circ}=\frac{160^{\circ}-x^{\circ}}{2}$

$51^{\circ}*2=\frac{160^{\circ}-x^{\circ}}{2}*2$

$102^{\circ}=160^{\circ}-x^{\circ}$

$102^{\circ}-160^{\circ}=160^{\circ}-160^{\circ}-x^{\circ}$

$-58^{\circ}=-x^{\circ}$

$x=58$

Therefore, the value of x is 58.

Answer 2

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