Question

finding arc measures involving an intersecting secant and tangent
what is the value of x?
x =
160°
x°
51°

Explanation:

Step1: Recall tangent-secant angle formula

The measure of an angle formed by a tangent and a secant outside a circle is half the difference of the measures of the intercepted arcs. So:
$$51^\circ = \frac{1}{2}(x^\circ - 160^\circ)$$

Step2: Multiply both sides by 2

Eliminate the fraction by multiplying each side by 2:
$$51^\circ \times 2 = x^\circ - 160^\circ$$
$$102^\circ = x^\circ - 160^\circ$$

Step3: Solve for x

Add $160^\circ$ to both sides to isolate $x$:
$$x^\circ = 102^\circ + 160^\circ$$
$$x^\circ = 262^\circ$$

Answer:

262