Pentagon Problem
posted by Mr Fahrenheit at
5:38 PM
Thursday, February 21, 2008
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19 Comments:
each angle = 45 degrees because if you connect each angle to a larger triangle then two of the segments are congruent so each triangle is iscosoles, so each base angle is congruent based on iscos. trangle therom (ITT) if each base angle is congrunt they must each = 45 degrees becasue all of the triangles are 45-45-90 traingles
so my final answer is
225
actually, since all the outside angles must add up to be 360, and there are five angles, that would divide out to be 71 and since they are Isosceles, 71 + 71= 142 subtract that from 180 to get 38, times 5 is equal to 190. so I think if I did that right is should be 190
Based on the drawing, due to the exterior angles theorem,stating that the sum of the exterior angles is 360 degrees, the lower angles on the iscosoles triangles is 72 degrees, and because the base angles on the triangle are always equal because of being an iscosoles triangle, 2 of the angles combined equals 144, and because all the angles in a triangle add up to 180 degrees, that leaves 36 degrees, therefor that is the top angle, multiply that 36 degrees by 5, and you get the total sum of the angles above, or 180 degrees.
This post has been removed by the author.
Hey Mcidiot Billbob, the ext. angles of any polygon is 180 not 360 so you're wrong
And Brennan Gills You're wrong because you can't assume they are 45 because it is an isos. Tri. because the two Congruent angles could be 46 and the other angle could be 88
POSTER---
Hint: Lean more towards the pentagon, hence the title. The pentagon with extending lines for sides (present in all ten-sided stars [not all ten-sided figures]) should be used.
Also, I mean adding the five INTERIOR angles. As in, the angles less than 180 degrees.
The answer is 180 degrees. With the interior angles of a pentagon adding up to 540 degrees, each individual angle must be 108 degrees. Therefore with the supplementary angles adding up to 180 degrees, each of the base angles of the iscosoles triangle will be 72 degrees. Simply take 180 minus 144, two multiplies by 72, and you get 36. This is the angle measurement of the top angle. Take 36 multiplied by 5 and you get 180 degrees.
there is nothing to suggest that the figure is regular so cannot assume isosceles triangles involved.
taking the exterior angles of the pentagon first clockwise and then anticlockwise gives 360 + 360 which is 720.
this is also the sum of the 2 angles at the base of the 5 triangles.
the total angles of 5 triangles is 5x180 which is 900.
subtracting 720 from this leaves 180 which is the sum of the required angles :)
this should be proof enough.
eric where did you go to school ?
POSTER---
Anon. above headcage: You're assuming that the star is regular, making the pentagon regular, which isn't the case. Right answer, wrong proof.
Headcage: Perfect!
thanks qae :)
This is my first post so it might be a little long. If we assume that the lines drawn are straight, then there are two geometric ideas that you need to use to solve this problem. the first is the interior angles of a polygon is equal to 180°*(n-2) where n = # of sides, the second is the sum of the angles on the same side of a straight line add to 180°. With this information, the sum total of all the interior angles in the five triangles will be 180°*5 or 900°. This will include the 10 angles at the base of the triangles or where the triangles touch the pentagon, angle EDF is one such angle. If we could simply subtract away the values of these base angles from the 900°, we would have the answer to the question. Angle EDF (one of the base angles)+ angle BDF (one of the angles in the pentagon) will equal 180°. Angle BDF will also be needed to when we look to subtract the value of angle CDB. We know that the sum of interior angles of the pentagon will be 180°(5-2)=540° and that we'll need to add twice this value to the 900° we have for the sum of the interior angles of the triangles. This total will be 1980°. From this total we will subtract the value of ten base angles and the ten interior angles of the pentagon (the five angles, we just use each of them twice). So the formula, in my opinion, is (180°*5)+(540°*2)-(180°*10) which turns out to be 180°. That's my opinion and I know this was a long winded explanation, if you need clarification let me know.
I have no idea! Im not that smart
JohnR said :
In My opinion, it is 360 degrees
Proof;
if you simply look at the star as if it was a circle, it would go around twice before arriving at the location at which it originated. That is 720 Deg. The angles which were added together are just the outside half the inside angles are not in the equation which would equal the other 360 degrees of the two (circles). so 360 is my answer
180 is wot i got
a=22.5 c= 45 e= 45 g=45 i =22.5
add to 180
thats using a protractor on the screen????
Triangle ADG and line AE:
180 - angle ADG = A + G = angle EDF
SO, angle EDF = A + G
Triangle CFI and Line EI:
180 - angle CFI = C + I = angle EFD
SO, angle EFD = C + I
Triangle EDF:
E + angle EDF + angle EFD = 180
E + A + G + C + I = 180
it's a star
180 is right
the angles are a 36 c 36 e 36 g 36
i 36
i did this by internal regular pantagon
108 are each of its angles so opposites are 108 adjacents 72
this left all external angles at 36
by 180 sum of triangles 72,72,36
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