Finding angles of the trapezoid

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RealSidi

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Hi, can anyone please help finding the values on the angles of the trapezoid in the image attached. AD and BC are equal. Any help is appreciated. Thanks!
(Sorry if my English is bad)20211104_173052.jpg
 
RealSidi said:
Hi, can anyone please help finding the values on the angles of the trapezoid in the image attached. AD and BC are equal. Any help is appreciated. Thanks!
(Sorry if my English is bad)View attachment 29550
Click to expand...
What do we know about angles in an isosceles trapezoid? If you are not sure, what about base angles in an isosceles triangle?
Does the problem say anything about DE? If nothing, then 40 degree angles is useless.
If DE is parallel to BC or same length as AD or BC, consider triangle ADE. Can you find the base angles?
 
lev888 said:
What do we know about angles in an isosceles trapezoid? If you are not sure, what about base angles in an isosceles triangle?
Does the problem say anything about DE? If nothing, then 40 degree angles is useless.
If DE is parallel to BC or same length as AD or BC, consider triangle ADE. Can you find the base angles?
Click to expand...
What do we know about angles in an isosceles trapezoid?
That opposite angles are equal. Same for the 2 lower angles if the triangle is isosceles, however I don't think we can prove that.

Yes I know how to solve the problem if the triangle is isosceles, but we would need to prove that first.

If you can help me prove that or have any other suggestions, that would be great.

Thanks in advance.
 
RealSidi said:
What do we know about angles in an isosceles trapezoid?
That opposite angles are equal. Same for the 2 lower angles if the triangle is isosceles, however I don't think we can prove that.

Yes I know how to solve the problem if the triangle is isosceles, but we would need to prove that first.

If you can help me prove that or have any other suggestions, that would be great.

Thanks in advance.
Click to expand...
The definition of isosceles trapezoid is:

In Euclidean geometry, an isosceles trapezoid is a convex quadrilateral with a line of symmetry bisecting one pair of opposite sides.

That definition tells you that due to symmetry, the base angles must be equal and the other two angles must be equal,

Read the response #2 over again and please answer all the questions posed.
 
RealSidi said:
What do we know about angles in an isosceles trapezoid?
That opposite angles are equal. Same for the 2 lower angles if the triangle is isosceles, however I don't think we can prove that.

Yes I know how to solve the problem if the triangle is isosceles, but we would need to prove that first.

If you can help me prove that or have any other suggestions, that would be great.

Thanks in advance.
Click to expand...
Please post an image that includes the diagram AND the question.
 
Subhotosh Khan said:
The definition of isosceles trapezoid is:

In Euclidean geometry, an isosceles trapezoid is a convex quadrilateral with a line of symmetry bisecting one pair of opposite sides.

That definition tells you that due to symmetry, the base angles must be equal and the other two angles must be equal
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Yes sorry, that's what I meant to say. Is there a way that this information helps us in solving the problem?
 
lev888 said:
Please post an image that includes the diagram AND the question.
Click to expand...
Please find attached the following two images. The question isn't in English so the 2nd imagine shows it translated in English.
 

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RealSidi said:
Please find attached the following two images. The question isn't in English so the 2nd imagine shows it translated in English.
Click to expand...
Ok, looks like a bad problem statement. I think you need to assume that DE is congruent to AD and BC.
Given this assumption, please draw a diagram showing all sets of equal angles.
 
lev888 said:
Ok, looks like a bad problem statement. I think you need to assume that DE is congruent to AD and BC.
Given this assumption, please draw a diagram showing all sets of equal angles.
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If that's the case, then it's easy, however my teacher told me that we cannot assume that, so is there a way to solve it without assuming?
 

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RealSidi said:
If that's the case, then it's easy, however my teacher told me that we cannot assume that, so is there a way to solve it without assuming?
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Ask your teacher why DE looks parallel to BC. If there are no constraints on DE then the diagram should look like the one in the attached image. Meaning the location of point E should be arbitrary, it should not be by some magic reason in the exact location that makes DE look parallel to BC. This is misleading.
 

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RealSidi said:
If that's the case, then it's easy, however my teacher told me that we cannot assume that, so is there a way to solve it without assuming?
Click to expand...
You can't assume anything from what it looks like in a picture; but in this case, unless you are told something beyond what is shown, the problem can't be solved.

Show your teacher these two examples, in which everything fits what you are told, but the angles are not the same:

1636407187889.png​

1636407416557.png​

If we do assume that DE is parallel to CB, then we can determine a unique solution. That is why we know the problem as shown is wrong.

1636407577002.png​
 
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