What's the angle?

Question

In the diagram below, ABC is a right triangle with right angle at C. The segments AD, DF, FE, EC, and CB are all of equal length. What is the size of angle A (in degrees)?

http://www.uidaho.edu/imc/gifs/07a.gif

goodanswer,

The problem did not state that segment DE was equal to the others. Try again. :-)

Hy,

Where did you determine that triangle EFC has a right angle in it? The picture is pretty much drawn to scale (but don't put a protractor on your screen to get the answer :-).

ScottR,

Please show your work. :-)

Answer 1

18

http://mudandmuck.com/str2/tri.gif
The angles in the picture are derived working from left to right (From angle A to the right)




90 - 3x + 2(90 - x) = 180
5x = 90
x = 18

Answer 2

Angle DAF = angle DFA = say A.

Therefore angle EDF = 2 A = Angle DEF (The exterior angle is the sum of the interior angle)
Angle DFE = 180 -4A.
Angle AFE = 180 - 3A

Therefore angle EFC = 3A =Angle ECF
Angle FEC = 180 -6A
Angle AEC =180 -4A

Therefore angle BEC = 4A.
Angle EBC = 4A

Angle A + angle B = 90.
5A = 90.

Therefore A = 18 degree.


Added after.
A tri angle has 6 elements (3 sides and 3 angles)

If any three of these 6 elements is given, then the other three can be found.

If two angles are given, then the third angle can be found. But only the ratio of the three sides can be found and not their exact value.

In the given figure angle C is marked as 90 degree. If the angle is marked with two perpendicular lines instead of curved lines then it means the angle is 90 degree.

If this angle is not given, then the angle A can have many values provided that the sum of the three angles is 180 degree.

Answer 3

I was unable to see the diagram. However, if it's a right triangle with all 3 sides of equal length, then the other 2 angles (other than the right angle) must be 45 degrees each. The sum of the 3 angles must be 180 degrees. If one angle is 90 degrees, the other two must add up to 90 degrees. If the legs are equal length, then both angles must be the same.

Answer 4

Okay, I'm a statistical analyst for a living, but slightly rusty in my geometry. But, I think there is a missing piece of information. Also, DE cannot be congruent to DF or DE. I think someone is trying to pull a fast one of you. Looks like

Answer 5

30 degrees. Since the stated segments are equal the angles in triangle DEF are equal each would be 60 degrees (60x3=180). The D angle in ADF is therefore 120 degrees. The other two angles in ADF are equal and both 30 degrees (180-120=60 60/2=30)

Answer 6

its 18.
The trick is that each of triangles with equal sides means that the angles opposite of the sides are equal, and realize the angles of a triangle equal to 180 degrees.

Answer 7

Fooled us, didn't you! Yes, I sailed in and worked out it was 30 deg, then checking found that would make triangle EFC isos with two base angles of 90 deg each. Impossible. The figure doesn't really exist.

Answer 8

180 - 2FAD = EDF
EDF = DEF = 180 - 2FAD

DFE = 180 - DEF - EDF = 180 - 2(180 - 2FAD)
DFE = 180 - 360 + 4FAD = -180 + 4FAD

180 - DFA - DFE = EFC; 180 - FAD - (-180 + 4FAD) = EFC
EFC = 180 - FAD + 180 - 4FAD = 3FAD

90 - ECF = ECB, ECB = 90 - 3FAD

2@ = 180 - ECB = 180 - (90 - 3FAD) = 90 + 3FAD
EBC = .5 (90 + 3FAD) = 45 + 1.5FAD

EBC + 90 + FAD = 180
45 + 1.5FAD + 90 + FAD = 180
2.5FAD = 180 - 45 - 90 = 45
FAD = 45 / 2.5 = 18 DEGREES

Answer 9

I thought that I had the answer, but the person who said that this figure can't exist is correct.

Answer 10

18degrees
let ^BCE=a
^ECF=90-a=^EFC
^FEC=180-(90-a)-(90-a)=2a
^DEF=180-^FEC-^BEC=90-3a/2=^EDF
^EFC=180-^EDF-^DEF=3a
^DFA=180-^DFE-^EFC=90-2a
^ADF=180-^DAF-^DFA=4a
^ADF+^EDF=180
therefore a=36degress
and angle A=^DAF=90-2a=18degrees