Question

what is the measure of circumscribed ∠x?

Explanation:

Step1: Recall the property of the sum of interior angles of a quadrilateral

The sum of the interior angles of a quadrilateral is \(360^{\circ}\). In the given figure, \( \angle VYW = 90^{\circ}\) (tangent - radius property) and \( \angle VWX=90^{\circ}\) (tangent - radius property), and \( \angle V = 90^{\circ}\) (given). Let \( \angle X=x\).

Step2: Apply the angle - sum formula for quadrilateral

We know that for quadrilateral \(VYWX\), \(\angle V+\angle VYW+\angle VWX+\angle X = 360^{\circ}\). Substituting the values: \(90^{\circ}+90^{\circ}+90^{\circ}+x = 360^{\circ}\). Simplifying the left - hand side gives \(270^{\circ}+x = 360^{\circ}\). Then \(x=360^{\circ}- 270^{\circ}=90^{\circ}\).

Answer:

\(90^{\circ}\)