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

Explanation:

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

The sum of interior angles of a pentagon is ((5 - 2)\times180^{\circ}=540^{\circ}).

Step2: Set up the equation

Let (\angle AFE=x). Then (62^{\circ}+44^{\circ}+70^{\circ}+60^{\circ}+43^{\circ}+x = 540^{\circ}).

Step3: Simplify the left - hand side

(62 + 44+70+60+43+x=(62 + 44)+(70 + 60)+43+x=106+130+43+x=279+x).

Step4: Solve for (x)

(279+x = 540), so (x=540 - 279=261) (This is wrong. Wait, actually, we should use the formula for the sum of exterior angles of a polygon. The sum of exterior angles of any polygon is (360^{\circ}). Let's re - do it.)

Let's use the property of the sum of exterior angles of a polygon. If we consider the angles around the non - overlapping parts related to the polygon formed by the transversals and parallel lines (assuming the lines are parallel as per the figure's nature).

We know that (\angle AFE+62^{\circ}+44^{\circ}+70^{\circ}+60^{\circ}+43^{\circ}=360^{\circ}) (sum of angles around a point - like situation considering the non - overlapping angles formed by the parallel lines and transversals).

(\angle AFE=360-(62 + 44+70+60+43))

(62+44 = 106), (106+70=176), (176+60 = 236), (236+43=279)

(\angle AFE=360 - 279=81^{\circ})

Answer:

(81^{\circ}) (corresponds to the second option)