Question

what is the value of u?
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Explanation:

Step1: Find the non - labeled interior angle adjacent to \(122^{\circ}\)

The sum of adjacent angles on a straight line is \(180^{\circ}\). Let the non - labeled interior angle be \(x\). Then \(x + 122^{\circ}=180^{\circ}\), so \(x = 180^{\circ}-122^{\circ}=58^{\circ}\).

Step2: Assume the triangle is isosceles (since no other information is given and the two non - \(u\) sides seem equal in the diagram)

In an isosceles triangle, the two non - vertex angles are equal. Let the other non - \(u\) angle (adjacent to \(H\)) be \(y\). Since the triangle is isosceles, \(y = x = 58^{\circ}\).

Step3: Use the triangle angle - sum property

The sum of angles in a triangle is \(180^{\circ}\). So \(u+58^{\circ}+58^{\circ}=180^{\circ}\). Then \(u=180^{\circ}-(58^{\circ}+58^{\circ})\).

$$u = 180^{\circ}-116^{\circ}=64^{\circ}$$

Answer:

\(64\)