Question

what is the value of x? x =

Explanation:

Step1: Recall the formula for the measure of an angle formed by a secant and a tangent.

The measure of an angle formed by a secant - tangent pair is half the difference of the intercepted arcs. Let the larger arc be $A_1 = 160^{\circ}$ and the smaller arc be $A_2=x^{\circ}$. The measure of the angle between the secant and the tangent is $51^{\circ}$. The formula is $\theta=\frac{1}{2}(A_1 - A_2)$.

Step2: Substitute the known values into the formula.

We have $51=\frac{1}{2}(160 - x)$.

Step3: Solve the equation for $x$.

First, multiply both sides of the equation by 2: $2\times51=160 - x$. So, $102 = 160 - x$.
Then, add $x$ to both sides: $102+x=160$.
Next, subtract 102 from both sides: $x = 160 - 102$.
$x = 58$.

Answer:

$58$