Question

properties of isosceles triangles
score: 2/5 penalty: 0.25 off
question
in △wxy, (overline{xy} cong overline{wx}) and (mangle w = 61^circ). find (mangle x).
answer attempt 1 out of 2
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Explanation:

Step1: Identify the type of triangle

Since \(\overline{XY}\cong\overline{WX}\) in \(\triangle WXY\), it is an isosceles triangle. In an isosceles triangle, the angles opposite the equal sides are equal. So, \(\angle Y=\angle W = 61^{\circ}\).

Step2: Use the triangle - angle sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). Let \(m\angle X=x\). Then, by the triangle - angle sum theorem \(m\angle W + m\angle X+m\angle Y=180^{\circ}\). Substitute \(m\angle W = 61^{\circ}\) and \(m\angle Y = 61^{\circ}\) into the equation: \(61^{\circ}+x + 61^{\circ}=180^{\circ}\).

Step3: Solve for \(x\)

Simplify the left - hand side of the equation: \(x+122^{\circ}=180^{\circ}\). Subtract \(122^{\circ}\) from both sides: \(x=180^{\circ}- 122^{\circ}\).

Answer:

\(58^{\circ}\)