Question

what is m∠u? m∠u =

Explanation:

Step1: Recall cyclic - quadrilateral property

In a cyclic quadrilateral, the sum of opposite angles is 180°. Angles ∠U and ∠S are opposite angles in the cyclic quadrilateral STUV. So, \((x + 90)+(x + 82)=180\).

Step2: Solve the equation for x

Combine like - terms: \(2x+172 = 180\). Subtract 172 from both sides: \(2x=180 - 172=8\). Divide both sides by 2: \(x = 4\).

Step3: Find the measure of ∠U

Substitute \(x = 4\) into the expression for ∠U. \(m\angle U=x + 90\). So, \(m\angle U=4 + 90=94^{\circ}\).

Answer:

94