Question

1. o is the centre of this circle and point t is a point of tangency. determine the value of $x^\circ$.

Explanation:

Step1: Recall tangent-radius property

A tangent to a circle is perpendicular to the radius at the point of tangency, so \(\angle OTS = 90^\circ\).

Step2: Use triangle angle sum

In \(\triangle OTS\), the sum of angles is \(180^\circ\). We know \(\angle OST = 35^\circ\) and \(\angle OTS = 90^\circ\). Let \(\angle x=\angle SOT\). Then \(x + 35^\circ+ 90^\circ=180^\circ\).

Step3: Solve for \(x\)

Simplify the equation: \(x=180^\circ - 35^\circ - 90^\circ\). Calculate \(180 - 35 - 90 = 55\), so \(x = 55^\circ\).

Answer:

\(55^\circ\)