ABCDE is a regular pentagon.

Question

DEF is a straight line.
Calculate

( a ) angle AEF,

Answer 1

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°.