Question

question
in △uvw, ( overline{vw} cong overline{uv} ) and ( mangle v = 159^{circ} ). find ( mangle u ).

Explanation:

Step1: Identify the triangle type

Since \(\overline{VW}\cong\overline{UV}\), \(\triangle UVW\) is an isosceles triangle. In an isosceles triangle, the base angles are equal. Let \(\angle U=\angle W = x\).

Step2: Use the triangle - angle sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(\angle U+\angle V+\angle W = 180^{\circ}\). Substitute \(\angle U = x\), \(\angle W=x\), and \(\angle V = 159^{\circ}\) into the equation: \(x + 159^{\circ}+x=180^{\circ}\).

Step3: Solve the equation for \(x\)

Combine like terms: \(2x+159^{\circ}=180^{\circ}\). Subtract \(159^{\circ}\) from both sides: \(2x=180^{\circ}- 159^{\circ}=21^{\circ}\). Then divide both sides by \(2\): \(x=\frac{21^{\circ}}{2}=10.5^{\circ}\).

Answer:

\(m\angle U = 10.5^{\circ}\)