Question

what is the measure of angle afe? 79° 81° 91° 99°

Explanation:

Step1: Use the formula for the sum of interior angles of a polygon

The sum of interior angles of a polygon with \(n\) sides is \((n - 2)\times180^{\circ}\). For a hexagon (\(n=6\)), the sum is \((6 - 2)\times180^{\circ}=720^{\circ}\). But here we can consider the sum of the angles around the "broken - line" (using the property of angles in a non - regular polygon - like figure formed by the parallel - like lines). The sum of the angles \(A + B + C+D + E+AFE=540^{\circ}\) (since we can think of it as a pentagon - like angle sum concept, or using the fact that if we extend the lines and use the properties of parallel - like lines and angles formed by transversals. Another way is to use the formula for the sum of angles in a polygon - like structure: \(\angle A+\angle B+\angle C+\angle D+\angle E+\angle AFE=(6 - 2)\times180^{\circ}\) (by considering the angles as part of a polygon - like figure with 6 "vertex - like" points, but subtracting the angles that are not part of the closed - angle sum. In fact, if we assume the figure is formed by three pairs of parallel lines (by the arrow directions), we can use the angle - sum property. Let \(\angle AFE=x\). Then \(62^{\circ}+44^{\circ}+70^{\circ}+60^{\circ}+43^{\circ}+x = 360^{\circ}\) (using the property that the sum of angles around a "loop" formed by the non - overlapping angles in the figure is \(360^{\circ}\) when considering the angles as parts of a full - circle - related angle sum (by extending the lines and using the fact that the exterior angles of a polygon - like figure sum up in a certain way).

Step2: Solve for \(x\)

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Answer:

\(81^{\circ}\)