Question

part 1 of 2

using the figure shown to the right, find the value of each variable.

x = (simplify your answer. do not include the degree symbol in your answer.)

Explanation:

Identify the geometric theorems

Using the Secant-Secant Angle Theorem and Inscribed Angle Theorem knowledge points

$$ \text{The angle outside the circle is formed by two secants intersecting at a point.} $$

Set up the equation for the exterior angle

Using the Secant-Secant Angle Theorem knowledge point

$$ 30^\circ = \frac{\text{Far Arc} - \text{Near Arc}}{2} $$

Solve for the near arc

Using the Secant-Secant Angle Theorem knowledge point

$$
LATEXBLOCK0
$$

Relate the inscribed angle to its intercepted arc

Using the Inscribed Angle Theorem knowledge point

$$
LATEXBLOCK1
$$

Answer:

Using the figure shown to the right, find the value of each variable.

\(x =\) <blank>10</blank> (Simplify your answer. Do not include the degree symbol in your answer.)