Question

find the value of $x$.

Explanation:

Step1: Recall exterior angle property

The measure of an angle formed by two tangents outside a circle is half the difference of the measures of the intercepted arcs. The major arc \(PR\) is \(142^\circ\), so the minor arc \(PR = 360^\circ - 142^\circ\).
Expression: \( \text{Minor arc } PR = 360 - 142 = 218^\circ \)

Step2: Calculate angle \(x\)

Use the tangent angle formula: \( x = \frac{1}{2} \times (\text{Minor arc } PR - \text{Major arc } PR) \)
Expression: \( x = \frac{1}{2} \times (218 - 142) \)

Step3: Simplify to find \(x\)

Compute the difference first, then multiply by \(\frac{1}{2}\).
Expression: \( x = \frac{1}{2} \times 76 = 38 \)

Answer:

\(38^\circ\)