ABCDE is a regular pentagon.
DEF is a straight line.
Calculate
( a ) angle AEF,
Since ABCDE is a regular pentagon, all its angles are equal.
Therefore, angle AED = 360° / 5 = 72°
Since DEF is a straight line, angles AED and DEF are supplementary.
Therefore, angle DEF = 180° - 72° = 108°
Angle AEF is half of angle DEF because triangle AEF is isosceles (AE = EF).
Therefore, angle AEF = 1/2 * 108° = 54°.