Question

question
in \\( \triangle t u v, \overline{v t} \cong \overline{u v} \\) and \\( \mathrm{m} \angle v=98^{\circ} \\). find \\( \mathrm{m} \angle u \\).

Explanation:

Step1: Identify the triangle type

Since \(\overline{VT}\cong\overline{UV}\), \(\triangle TUV\) is an isosceles triangle. In an isosceles triangle, the angles opposite the equal sides are equal. So \(\angle T=\angle U\).

Step2: Use the triangle - angle sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). Let \(m\angle U = x\) and \(m\angle T=x\) (because \(\angle T = \angle U\)), and \(m\angle V = 98^{\circ}\). Then, by the angle - sum formula \(m\angle T+m\angle U+m\angle V=180^{\circ}\), we substitute the values: \(x + x+98^{\circ}=180^{\circ}\).

Step3: Solve the equation for \(x\)

Combine like terms: \(2x+98^{\circ}=180^{\circ}\). Subtract \(98^{\circ}\) from both sides: \(2x=180^{\circ}-98^{\circ}=82^{\circ}\). Divide both sides by 2: \(x = 41^{\circ}\).

Answer:

\(41^{\circ}\)