Question

what is the value of x? x =

Explanation:

Step1: Use the formula for the angle formed outside a circle

The measure of an angle formed outside a circle is $\frac{1}{2}$ the difference of the measures of the intercepted arcs. The formula is $\text{Angle}=\frac{1}{2}(\text{Large arc}-\text{Small arc})$. Here, the angle is $51^{\circ}$, the large arc is $160^{\circ}$, and the small arc is $x^{\circ}$. So, $51=\frac{1}{2}(160 - x)$.

Step2: Solve the equation for $x$

Multiply both sides of the equation by $2$: $51\times2=160 - x$. So, $102 = 160 - x$.
Then, add $x$ to both sides: $102+x=160$.
Subtract $102$ from both sides: $x = 160 - 102$.

Answer:

$58$