Question

figure vwxy ≅ figure uhfi. what is m∠u?
(there are two quadrilaterals, vwxy and uhfi, with angle measures at some vertices. the first quadrilateral has angles at v: 81°, at w: 119°, at y: 83°. the second quadrilateral has angles at f: 91°, at i: 93°. then it asks for m∠u = °)

Explanation:

Step1: Use the property of congruent polygons

Since \(VUWX\cong HGFI\), corresponding angles are equal.

Step2: Find the measure of \(\angle Q\)

The sum of interior angles of a quadrilateral is \(360^{\circ}\). In quadrilateral \(VUWX\), \(\angle V = 91^{\circ}\), \(\angle W=110^{\circ}\), \(\angle X = 84^{\circ}\). Let \(\angle U=x\). Then \(91^{\circ}+110^{\circ}+84^{\circ}+x = 360^{\circ}\).

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Since \(\angle U\) and \(\angle Q\) are corresponding angles (because \(VUWX\cong HGFI\)), \(m\angle Q=75^{\circ}\)

Answer:

\(75\)