Degree of an angle on a kite

[shebabe44]

I have a kite, the angle at the top is 75, both sides are 50, what is the angle at the bottom?

Many thanks in advance.

[boxtops]

Is this homework?

The angles in a given triangle must add up to 180 degrees, and a traditionally shaped kite can be divided into two triangles. I don't know what you mean by "both sides are 50".

[shebabe44]

Thank for for your help the angle on the right side of the kite is 50 and the angle adjacent is also 50. I am struggling here.

[boxtops]

is it a normal diamond-shaped kite?

[shebabe44]

Yes it is a normal shaped kite

[dundurn]

interior angles of a quadrilateal add to 360 - so 360 -50 - 50 -75 = 185

on the other hand this would make for a very unusual kite - are you sure you havethe correct measurements?

[boxtops]

dundurn I am so glad you posted, I got 185 degrees but that makes it almost flat at the bottom!

[Prudie]

If you mean a real kite you must give the dimension either from the top to the bottom or at least the length of the longer sides. From your question the top triangle can have any sized triangle at the bottom

[boxtops]

Prudie that shouldn't make a difference, the four angles will still add up to 360 degrees however big it is?

[Prudie]

Yes they will but we only have 75 at the top which makes each base angle 52.5 (180 - 90-75/2) and sides I assume of length 50. That only gives us the top triangle. The bottom could be anything

[boxtops]

No, the length isn't 50, I checked that with shebabe - 50 is the angle of the two side angles. My calculations agree with dundurn, 50+75+50 - 175 leaving 185 degrees for the base angle.

[Mamyalynne]

well then it most definitely is not a diamond shape then.

[Prudie]

Well if 50 is the base angle that must mean the angle between the top side and the horizontal base which still means the bottom triangle could be anything. If it is actually the whole of the side angles is 50, as that is acute it couldn't possibly be drawn as a kite. Difficult to do when we can't draw on here isn't it.

[Mamyalynne]

yes if the side angles are indeed 50 degrees then it would end in a point and that would not be possible to make 185, something is wrong here. My brain is starting to hurt!!

[Prudie]

Yes something is wrong. Lets forget it's a kite and say it's a quadrilateral. If we have been given 3 angles of 75, 50 and 50 then yes the 4th angle is 185. Now try drawing that, it's like a boomerang ie the bottom anle of 185 reflexes on itself.

[Mamyalynne]

Its the 50 degrees that I think is incorrect, I also suspect they are lengths.

[boxtops]

shebabe says not, in her second post. The grey matter is definitely struggling, we could do with a sketch pad!

[alexanderd]

I could do with a drink!!

[alavahalf]

I've got a kite and it does'nt give me these kind of problems ... you just make sure you've got your name and address in your pocket so someone can identify the body.

[razza]

Why do you want to know

[johnny.5]

so it could well be an arrow-head shaped kite