Question

find the value of x.

x =

Explanation:

Step1: Use the theorem of the angle formed by a tangent and a secant

The measure of an angle formed by a tangent and a secant is half the difference of the measures of the intercepted arcs. Also, the sum of the measure of an inscribed angle and the angle formed by the tangent - secant is related. Here, we use the property that \(x=\frac{1}{2}(m\overset{\frown}{PTQ}-m\overset{\frown}{PQ})\). But another way is to use the property that \(x = 90^{\circ}-\frac{1}{2}\times50^{\circ}\) (based on the relationship between the angle at the vertex \(S\) and the inscribed angle \(x\)).

Step2: Calculate the value of \(x\)

$$
LATEXBLOCK0
$$

Answer:

\(65\)