Problem:
In the diagram below, points A,E and F lie on the same line. If ABCDE is a regular pentagon, and angle EFD=90 degrees, then how many degrees are in the measure of FDE?
∠DEF is an exterior angle of pentagon ABCDE.
The sum of all exterior angles in a polygon = 360º
Since ABCDE is a regular pentagon, all 5 of its exterior angles have the same measure.
So..the measure of one exterior angle = 360° / 5 = 72°
m∠DEF = 72°
Since there are 180° in every triangle...
m∠DEF + m∠EFD + m∠FDE = 180°
72° + 90° + m∠FDE = 180° Subtract 72° and 90° from both sides.
m∠FDE = 18°
∠DEF is an exterior angle of pentagon ABCDE.
The sum of all exterior angles in a polygon = 360º
Since ABCDE is a regular pentagon, all 5 of its exterior angles have the same measure.
So..the measure of one exterior angle = 360° / 5 = 72°
m∠DEF = 72°
Since there are 180° in every triangle...
m∠DEF + m∠EFD + m∠FDE = 180°
72° + 90° + m∠FDE = 180° Subtract 72° and 90° from both sides.
m∠FDE = 18°