Question

question
in the diagram below, quadrilateral tuwv is inscribed in circle x. find the measure of ∠v.
answer attempt 2 out of 6
m∠v = 130

Explanation:

Step1: Recall cyclic quadrilateral property

In a cyclic quadrilateral (a quadrilateral inscribed in a circle), opposite angles are supplementary, i.e., their sum is \(180^\circ\). Let \(\angle T = 50^\circ\) (from the diagram, assuming the angle at \(T\) is \(50^\circ\)) and \(\angle V\) be the angle we need to find. Since \(\angle T\) and \(\angle V\) are opposite angles in cyclic quadrilateral \(TUWV\), we have \(\angle T+\angle V = 180^\circ\).

Step2: Solve for \(\angle V\)

Substitute \(\angle T = 50^\circ\) into the equation: \(50^\circ+\angle V=180^\circ\). Subtract \(50^\circ\) from both sides: \(\angle V = 180^\circ - 50^\circ=130^\circ\).

Answer:

\(130^\circ\)