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quadrilateral vwxy is a kite. what is m∠w?
w
x
110°
v
128°
y
m∠w =
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Explanation:

Step1: Recall the sum of interior angles of a quadrilateral

The sum of the interior angles of a quadrilateral is \(360^{\circ}\). So, \(m\angle W + m\angle X+ m\angle V + m\angle Y=360^{\circ}\).

Step2: Use the property of a kite

In a kite, two pairs of adjacent sides are equal. Also, one pair of opposite angles (the angles between the unequal sides) are equal. Here, \(\angle X\) and \(\angle V\) are given, and \(\angle W=\angle Y\).
Let \(m\angle W = x\). Then \(x + 110^{\circ}+128^{\circ}+x=360^{\circ}\).
Combine like - terms: \(2x+238^{\circ}=360^{\circ}\).
Subtract \(238^{\circ}\) from both sides: \(2x=360^{\circ}- 238^{\circ}=122^{\circ}\).
Divide both sides by 2: \(x = 61^{\circ}\).

Answer:

\(61\)