Question

what is the value of u?

Explanation:

Step1: Use the property of angles around a point

The sum of angles around a point is \(360^{\circ}\). But we can also use the fact that the sum of angles on a straight - line is \(180^{\circ}\). However, another approach is to note that the sum of the given angles and \(u\) (since they are angles around a point) can be calculated. But a more straightforward way is to use the property of vertical angles and angle addition.

We know that the sum of angles in a full - circle (around a point) is \(360^{\circ}\). But we can also use the fact that if we consider the non - overlapping angles: \(u + 105^{\circ}+44^{\circ}+ \text{(other angles)}\). But a better way is to use the property that the sum of angles around a point: \(u+105^{\circ}+44^{\circ}+ \text{(vertically opposite angles sum)}\).

Alternatively, we can use the fact that \(u + 105^{\circ}+44^{\circ}= 180^{\circ}\) (if we consider a straight - line). Wait, no. Let's re - think.

We know that the sum of angles around a point is \(360^{\circ}\). But if we consider that the angles are formed by intersecting lines. Let's use the property of adjacent angles.

We know that \(u+105^{\circ}+44^{\circ}=180^{\circ}\) (because they are angles on a straight - line).

Step2: Solve for \(u\)

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Answer:

\(31^{\circ}\)