Question

given that ( mangle t = 35^{circ} ) and ( mangle e = 125^{circ} ), what is the measure of ( angle u )?
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the measure of ( angle u ) is ( square ) degrees.

Explanation:

Step1: Recall the formula for the sum of interior angles of a quadrilateral

The sum of interior angles of a quadrilateral is \(360^{\circ}\). Let the quadrilateral be \(T - E - U-\) (assuming the fourth angle is \(V\)). So, \(m\angle T+m\angle E + m\angle U+m\angle V=360^{\circ}\). In a trapezoid (assuming it is a trapezoid, since \(T\) and \(E\) are angles of a quadrilateral and we can use the property of adjacent - angles in a trapezoid: \(\angle T\) and \(\angle V\) are adjacent angles, \(\angle E\) and \(\angle U\) are adjacent angles. Also, if it is a trapezoid, \(m\angle T + m\angle V=180^{\circ}\) and \(m\angle E + m\angle U=180^{\circ}\) (because of the property of consecutive - interior angles for parallel lines).

Step2: Solve for \(m\angle U\)

We know that \(m\angle E + m\angle U=180^{\circ}\) (property of consecutive - interior angles in a trapezoid). Given \(m\angle E = 125^{\circ}\), then \(m\angle U=180^{\circ}-m\angle E\).
Substitute \(m\angle E = 125^{\circ}\) into the formula: \(m\angle U=180 - 125\).

Answer:

\(55\)