Question

what is the value of x in the diagram?

Explanation:

Step1: Use the formula for the angle formed by a secant and a tangent

The formula is \( \angle C=\frac{1}{2}(\text{major arc}-\text{minor arc}) \). Here, \( \angle C = 50^{\circ} \), major arc \(=200^{\circ}\), minor arc \(=x\).

Step2: Substitute values into the formula

\(50=\frac{1}{2}(200 - x)\)
Multiply both sides by 2: \(100=200 - x\)

Step3: Solve for \(x\)

\(x = 200 - 100\)

Answer:

\(x = 100\)