Answer: The correct option is (D) ∠FBE.
Step-by-step explanation: Given that ∠FAE measures 72° in the figure.
We are to find the other angle that measure 72°.
We know that angles subtended by the same arc (chord) on the circumference of a circle have equal measures.
∠FAE is an angle subtended by the arc FE on the circumference of the circle at the point 'A'.
The other angle subtended by the arc FE on the circumference of the circle is
∠FBE at the point 'B'.
Therefore, we must have
m∠FAE = m∠FBE.
Since, m∠FAE = 72°, so m∠FBE = 72°.
Thus, the other angle that measures 72° is ∠FBE.
Option (D) is correct.