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in △vwx, (overline{vw} cong overline{xv}) and (mangle x = 22^circ). find (mangle v).
answer attempt 2 out of 2
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Explanation:

Step1: Recall the property of isosceles triangles

In a triangle, if two sides are congruent (\(\overline{WX}\cong\overline{XV}\)), then the triangle is isosceles. In an isosceles triangle \(\triangle VWX\) with \(\overline{WX}\cong\overline{XV}\), the base - angles are congruent. The sum of the interior angles of a triangle is \(180^{\circ}\). Let \(m\angle V = m\angle W=x\).

Step2: Set up the angle - sum equation

We know that \(m\angle X + m\angle V + m\angle W=180^{\circ}\). Since \(m\angle X = 22^{\circ}\) and \(m\angle V=m\angle W\), we substitute into the equation: \(22^{\circ}+x + x=180^{\circ}\).

Step3: Solve the equation for \(x\)

Combine like terms: \(22^{\circ}+2x = 180^{\circ}\). Subtract \(22^{\circ}\) from both sides: \(2x=180^{\circ}- 22^{\circ}=158^{\circ}\). Divide both sides by 2: \(x=\frac{158^{\circ}}{2}=79^{\circ}\).

Answer:

\(79^{\circ}\)