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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?

Guest Aug 1, 2017

Best Answer 

 #1
avatar+7324 
+3

∠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°

hectictar  Aug 2, 2017
 #1
avatar+7324 
+3
Best Answer

∠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°

hectictar  Aug 2, 2017

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