Solving Quadrilaterals with Known Angles & 1 Side

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In summary, there is no formula to solve for the lengths of the other three sides of a quadrilateral when all four angles and one side are known. This is because the shape of the quadrilateral cannot be determined solely by the given information. Even in the case of a rectangle, knowing one side and all four angles does not determine the other three sides. Therefore, there can be an infinite number of possibilities for the lengths of the other sides.
  • #1
Physics is Phun
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to solve a quadrilateral when you know all four angles and one side? I can't seem to find any way to solve the other 3 sides in this one question I am working on.
thanks :biggrin:
 
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  • #2
seems that it should be determined by that data, i.e. the shape should be determiend and then you have one side to set the scale, provided you know which two angles the given side is between. but a formula has not come to mind yet for their lengths.


Wait! what about a rectangle!?
 
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  • #3
No, it's not possible. For example, suppose that all of the angles were right angles. You have one side's length, but how would you know whether the figure is a square or a rectangle? You can't. Suppose the side you are given has length 1, and all the angles are right. The side across from the given side must be 1, but the other two could be anything.
 
  • #4
mathwonk said:
Wait! what about a rectangle!?

Or any other quadrilateral for that matter:

assume that the fixed side is length one and as drawn in the plane is the interval [0,1] on the x axis. extend the sides incident to the ends of this segment to infinity, and draw any line parallel to the side "opposite" our fixed side, then all angles are the same and the other sides can be an uncountable number of options.
 
  • #5
yeah that mental picture conviced me but i thought i would just mention the easy one.
 

Related to Solving Quadrilaterals with Known Angles & 1 Side

1. What is a quadrilateral?

A quadrilateral is a polygon with four sides and four angles.

2. What are the known angles and side of a quadrilateral?

The known angles and side of a quadrilateral refer to the measurements of the four angles and one side that are given in a problem that involves solving for the remaining angles and side.

3. How do you solve a quadrilateral with known angles and side?

To solve a quadrilateral with known angles and side, you can use various methods such as the angle sum property, the exterior angle sum property, and the properties of parallel lines and transversals.

4. Can a quadrilateral have more than one solution?

Yes, a quadrilateral can have more than one solution as long as it satisfies the given angles and side measurements. However, some quadrilaterals may not have a valid solution.

5. What is the importance of solving quadrilaterals with known angles and side?

Solving quadrilaterals with known angles and side can help us determine the missing measurements of a shape, which can be applied in various fields such as geometry, engineering, and architecture.

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