Question

find y in the diagram below

Explanation:

Step1: Identify the exterior angle property

The angle of \(119^\circ\) is an exterior angle to the triangle, and it is equal to the sum of the two non - adjacent interior angles. But in this case, if we assume that \(EF\parallel AB\) (since the diagram seems to suggest parallel lines, maybe alternate interior angles or exterior angle - interior angle relationship), the angle adjacent to \(119^\circ\) on the straight line \(CB\) is \(180 - 119=61^\circ\). Wait, actually, if we consider the triangle, and if \(EF\) and \(AB\) are parallel, then the angle \(y\) and the angle supplementary to \(119^\circ\) might be related. Wait, the correct approach: the angle at \(E\) adjacent to \(119^\circ\) is \(180 - 119 = 61^\circ\). But if the triangle is isosceles or if we have parallel lines, but more likely, using the exterior angle theorem or the fact that the angle \(119^\circ\) is equal to \(180 - y\) (if \(AB\parallel EF\), then consecutive interior angles are supplementary). Wait, let's correct: If we assume that \(EF\parallel AB\), then \(\angle FEB+\angle EBA = 180^\circ\) (consecutive interior angles). But \(\angle FEB = 119^\circ\), so \(\angle EBA=y = 180 - 119=61^\circ\)? Wait, no, maybe the triangle has \(EF\) and \(AB\) such that the angle at \(E\) is \(119^\circ\), and the angle at \(B\) is \(y\), and since \(CEB\) is a straight line, the angle inside the triangle at \(E\) is \(180 - 119 = 61^\circ\). But if the triangle is isosceles or if we have some parallelism, but the most straightforward is that the angle \(119^\circ\) and \(y\) are related by the fact that \(119^\circ=180^\circ - y\) (if \(AB\parallel EF\), alternate exterior - interior angles? Wait, no, let's think again. The angle of \(119^\circ\) is an exterior angle, so it should be equal to the sum of the two remote interior angles. But if one of the interior angles is \(y\) and the other is equal to \(y\) (if the triangle is isosceles), but that might not be the case. Wait, the correct way: the angle adjacent to \(119^\circ\) on the straight line is \(180 - 119 = 61^\circ\). If we assume that the triangle is isosceles with \(EB = BA\) (not sure), but more likely, the diagram is such that \(EF\parallel AB\), so the corresponding angles or consecutive interior angles. Wait, the answer is likely \(y = 180 - 119=61^\circ\)? Wait, no, maybe I made a mistake. Wait, the exterior angle theorem: the exterior angle is equal to the sum of the two non - adjacent interior angles. But if the triangle has angles \(y\), \(y\), and the exterior angle \(119^\circ\), then \(119 = y + y\)? No, that would be \(y = 59.5\), which is not likely. Wait, maybe the diagram is a triangle with a transversal, and \(EF\) and \(AB\) are parallel, so the angle \(119^\circ\) and \(y\) are supplementary? Wait, no, consecutive interior angles are supplementary. So if \(EF\parallel AB\), then \(\angle FEB+\angle EBA = 180^\circ\). So \(119 + y=180\), so \(y = 180 - 119 = 61^\circ\).

Step1: Use supplementary angles (straight line)

The angle \(\angle FEC = 119^\circ\) and \(\angle FEB\) are supplementary (since \(C\), \(E\), \(B\) are colinear). So \(\angle FEB=180^\circ - 119^\circ = 61^\circ\).

Step2: Use parallel lines (assumed \(EF\parallel AB\))

If \(EF\parallel AB\), then \(\angle FEB=\angle EBA\) (alternate interior angles). So \(y = 61^\circ\).

Answer:

\(y = 61^\circ\)