Question

finding arc measures involving an intersecting secant and tangent. what is the value of x? x =

Explanation:

Step1: Recall the formula

The measure of the angle formed by a secant - tangent intersection outside a circle is given by $\frac{1}{2}(m\overset{\frown}{major}-m\overset{\frown}{minor})$. Here, the angle is $51^{\circ}$, the major arc is $160^{\circ}$ and the minor arc is $x^{\circ}$. So, $51=\frac{1}{2}(160 - x)$.

Step2: Solve the equation

Multiply both sides of the equation by 2: $2\times51=160 - x$. So, $102 = 160 - x$.

Step3: Isolate x

Add $x$ to both sides: $102+x=160$. Then subtract 102 from both sides: $x = 160 - 102$.

Answer:

$x = 58$